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Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a circle of radius 5 cm. Construct a pair of tangents to it, the angle between which is \(60^o \).Measure the distance between the centre of the circle and the point of intersection of the tangents.
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Steps of construction:
1. Draw circle with centre O and radius OA = 5 cm, .
Mark another point B on the circle such that AOB = 120°, supplementary to the angle between the tangents. Since the angle between the tangents to be constructed is 60°.
.
3. Construct angles of 90° at A and B and extend the lines so as to intersect at point P.
4. Thus, AP and BP are the required tangents to the circle.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of Construction:
Step I: A line segment AB of 8 cm is drawn.
Step II: With A as centre and radius equal to 4 cm, a circle is drawn which cut the line at point O.
Step III: With B as a centre and radius equal to 3 cm, a circle is drawn.
Step IV: With O as a centre and OA as a radius, a circle is drawn which intersect the previous two circles at P,Q and R, S.
Step V: AP, AQ, BR and BS are joined.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a parallelogram \( ABCD\) in which \(BC=5\ cm,\ AB=3\ cm \) and \(\angle ABC=60^o \). Divide it into triangles \(BCD \) and \(ABD \) by the diagonal \(BD \). Construct the \( \triangle BD’C’\) similar to \(\triangle BDC \) with scale factor \(\dfrac{4}{3} \). Draw the line segment D’A’ parallel to DA, where A’ lies on extended side BA. Is A’BC’D’ a parallelogram?
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of constructions:
1. Draw a line AB=3 cm.
2. Draw a ray BY making an acute ∠ABY=60°.
3. With centre B and radius 5 cm, draw an arc cutting the point C on BY.
4. Draw a ray AZ making an acute ∠ZAX’=60°.(BYAZ, ∠YBX’=ZAX’=60°)
5. With centre A and radius 5 cm, draw an arc cutting the point D on AZ.
6. Join CD
7. Thus we obtain a parallelogram ABCD.
8. Join BD, the diagonal of parallelogram ABCD.
9. Draw a ray BX downwards making an acute ∠CBX.
10. Locate 4 points on , such that .
11. Join and from draw a line intersecting the extended line segment at .
12. Draw C’D’ CD intersecting the extended line segment BD at D’. Then, D’BC’ is the required triangle whose sides are 4/3 of the corresponding sides of DBC.
13. Now draw a line segment D’A’ DA, where A’ lies on the extended side BA.
14. Finally, we observe that A’BC’D’ is a parallelogram in which A’D’= 6.5 cm A’B = 4 cm and A’BD’= 60° divide it into triangles BC’D’ and A’BD’ by the diagonal BD’.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct a pair of tangents to a circle of radius 4 cm inclined at an angle of \(45^o \).
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Step 1: Place the compass on a point O and draw a circle with radius = 4 cm.
Step 2: Take any point A on the circle. Draw ray OA.
Step 3: Place the compass on point A and draw two equidistant arcs on line OA to intersect OA in points D and E.
Step 4: From point D, mark two arcs above and below line OA. Similarly, mark two arcs from point E such that they intersect the arcs marked from point D.
Step 5: Join the intersection points of the arcs to obtain one tangent from A.
Step 6: Draw ray OB such that .
Step 7: Repeat steps 3,4 and 5 for point B in place of point A to obtain the tangent at point B
Step 8: Let the tangent from point B intersect the tangent from point A at point P.
PA and PB are the required tangent. The angle between PA and PB is .
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct two circles of radii 3 cm and 4 cm whose centres are 8 cm apart. Draw the pair of tangents from the centre of each circle to the other circle.
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Steps of construction :
(1) Draw a line segment .
(2) Taking as centre and radius 4 cm draw a circle.
(3) Taking as centre and radius 3 cm draw another circle.
(4) Draw perpendicular bisector of which intersects at M.
(5) Taking M as center and radius draw another circle.
(6) Taking as centre and radius 4 – 3 = 1 cm draw a circle which intersects the circle center M at P and Q.
(7) Join and and produce to intersect the given circle at A and A’.
(8) From point draw and .
(9) Join AB and A’B’
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct a triangle \(ABC \) in which \(AB=5\ cm,\ \angle B=60^o \) and the altitude \(CD=3\ cm \). Then construct another triangle whose sides are \(\dfrac{3}{4} \) times the corresponding sides of \( \triangle ABC\).
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Steps of construction :
1. Draw a ray BX making an acute angle with BC on opposite side of vertex A.
2. Locate 4 points (as 4 is greater in 3 and 4). on line segment BX.
3. Join and draw a line through , parallel to intersecting BC at C’.
4. Draw a line through C’ parallel to AC intersecting AB at A’. DA’BC’ is the required triangle.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths
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Construct a circle with radius = 6 cm and centre be C
Locate a point A which is 10 cm from C
Then find the perpendicular bisector of line joining points C and A. lets say the mid point will be M.
Now draw an ‘another circle with centre at M and radius and lets say this circle cuts the previous circle at
points N and Q then draw the lines AB and AN which are our external tangents.
Sinces is right angle triangle at
Therefore using pythagoras theorem
is the length of the tangent.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are \(\dfrac{5}{3} \) times the corresponding sides of the given triangle.
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Steps of Constructions:
1. Draw a right angle triangle ABC right angled at B, AB = 3 cm and BC = 4 cm.
2. Draw an acute angle CBX with BC and make five equal arc on it and such that
3. Join to C.
4. Through draw a parallel line to . This line intersects BC produced at point C’.
5. Through C’ draw a parallel line to AC. This line intersects the line AB produced at point A’.
Thus, triangle A’BC’ is the required triangle similar to triangle ABC.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct a triangle \(ABC \), in which base \(BC=6\ cm,\ \angle BC=60^o \) and \(\angle BAC=90^o \). Then construct another triangle whose sides are \(\dfrac{3}{4} \) of the corresponding sides of \( \triangle ABC\).
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The A’BC’ whose sides are of the corresponding sides of ABC can be drawn as follows:
Step 1: Draw a with side
Step 2: Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
Step 3: Locate 4 points, on line segment BX.
Step 4: Join and draw a line through , parallel to intersecting BC at C’.
Step 5: Draw a line through C′ parallel to AC intersecting AB at A′ .
The triangle A′ BC′ is the required triangle.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a pair of tangents to a circle of radius 3.5 cm which are perpendicular to each other.
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Steps of construction
Step I. Draw a circle of any convenient radius with O as centre.
Step II. Take a point A on the circumference of the circle and join OA. Draw a perpendicular to OA at point A.
Step III. Draw a radius OB, making an angle of 90° with OA.
Step IV. Draw a perpendicular to OB at point B Let both the perpendicular intersect at point P
Step V. Join OP PA and PB are the required tangents, which make an angle of 45° with OP.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a \(\triangle ABC \) with \(BC=8\ cm.\ \angle ABC=45^o \) and \(\angle BAC=105^o \). Then construct a triangle whose sides are \(\dfrac{4}{3} \) times the corresponding sides of the \(\triangle ABC \).
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Suppose BX and CY intersect at A. ABC so obtained is the given triangle.
To construct a triangle similar to ABC, we follow the following steps.
STEP I Construct an acute angle CBZ at B on opposite side of vertex A of ABC.
STEP II Markoff four (greater 4 of and 3 in ) points on BZ such that .
STEP III Join (the third point) to C and draw a line through parallel to , intersecting the extended line segment BC at C.
STEP IV Draw a line through C parallel to CA intersecting the extended line segment BA at A.
Triangle ABC so obtained is the required triangle such that
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a triangle \( ABC\) with side \(BC=7\ cm,\ \angle B=45^o, \) and \(\angle A=105^o \). Then construct another triangle whose sides are \(\dfrac{3}{4} \) times the corresponding sides of \(\triangle ABC \).
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Constructing ABC:
Step 1: Draw base BC of length 7 cm.
Step 2: Draw a ray at an angle of with line BC from point B.
Step 3: Draw a ray at an angle of from line CB from point C and mark the intersection point of the rays from B and C as A.
Step 4: Join A – B and A – C.
ABC is the required triangle.
For constructing
Step 1: Draw a ray BX at an acute angle to line BC on the opposite side of A.
Step 2: Mark 4 equidistant points on ray BX.
Step 3: Join and .
Step 4: Draw parallel to and label the intersection on the extension of BC as D.
Step 5: Draw DE parallel to BA and label the intersection with the extension of BA as E.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of \(60^o \).
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1) Draw a circle of radius 5 cm.
2) Draw horizontal radius OQ.
3) Draw angle from point O. Let the ray of angle intersect the circle at point R.
4) Now draw from point Q.
5) Draw from point R.
6) Where the two arcs intersect, mark it as point P.
Therefore, PQ and PR are the tangents at an angle of .
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a \(\triangle ABC \) with sides \(BC=6\ cm,AB=5\ cm \) and \(\angle ABC=60^o \). Construct a \( \triangle A’BC’\) similar to \(\triangle ABC \) such that sides of \(\triangle ABC \) are \( \dfrac{3}{4}\) of the corresponding sides of \(\triangle ABC \).
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The A’BC’ whose sides are of the corresponding sides of ABC can be draw as follows:
Step 1: Draw a with side
Step 2: Draw a ray BX making an acute angle with BC on the opposite side of vertex A.
Step 3: Locate 4 points, on line segment BX.
Step 4: Join and draw a line through , parallel to intersecting at .
Step 5: Draw a line through C’ parallel to AC intersecting AB at A’.
The triangle A’BC’ is the required triangle.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw two tangents to a circle of radius 3.5 cm from a point P at a distance of 6 cm from its centre O.
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Steps of Construction :
1. Draw a circle of radius 3.5 cm from centre point O
2. Set a point P which is located at distance 6.2 cm from point O. Join OP.
3. Draw a perpendicular bisector of OP which cuts OP at point Q.
4. Now, considering Q as a centre and equal radius (OQ = PQ).Draw a circle.
5. Both circles intersect at points A and B.
6. Join PA nd PB.
Therefore, AP and BP are the required tangents.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a right triangle in which the sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the given triangle.
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of constructions :
1. Draw a line segment BC = 8 cm.
2. Draw line segment BX making an angle of 90º at the point B of BC.
3. From B mark an arc on BX at a distance of 6 cm, Let it is A.
4. Join A to C.
5. Making an acute angle draw a line segment BY from B.
6. Mark on BX such that .
7. Joint to .
8. Draw a line segment to to meet BC at C’.
9. Draw line segment CA’  to CA to meet AB at A’
A’BC’ is the required triangle.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct a \(\triangle ABC \) in which \(BC=6.5\ cm,\ AB=4.5\ cm \) and \(\angle ABC=60^o \). Construct a triangle similar to this triangle whose sides are \(\dfrac{3}{4} \) of the corresponding sides of the triangle \(ABC \).
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of constructions :
(i) Construct a in which .
(ii) At B draw an acute angle CBX below base BC.
(iii) Along BX, mark off points , such that .
(iv) Join .
(v) From draw meeting produced part of BC at C.
(vi) From C’, draw C’ A’  C A intersecting the extended line segment BA at A’.
Thus, A’B’C’ is the required triangle each of whose sides is 3/2 times the corresponding sides of the triangle ABC.
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Draw a circle of radius 3 cm. From a point P, 7 cm away from its centre, construct a pair of tangents to the circle. Measure the lengths of the tangents.
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of construction :
1. Draw a line segment PO = 7 cm.
2. From the point O, draw a circle of radius = 3 cm.
3. Draw a perpendicular bisector of PO. Let M be the midpoint of PO.
4. Taking M as centre and OM as radius draw a circle.
5. Let this circle intersects the given circle at the point Q and R.
6. Join PQ and PR.
On measuring we get
PQ = PR = 6.3 cm
Write ‘T’ for true and ‘F’ for false statement. In each case, give reason for your answer.
Construct a \(\triangle ABC \) in which \(BC=9\ cm,\ \angle B=60^o \) and \(AB=6\ cm \). Then construct another triangle whose side are \(\dfrac{2}{3} \) of the corresponding sides of \(\triangle ABC \)
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This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
Steps of constructions :
(i) Construct a in which .
(ii) At B draw an acute angle CBX below base BC.
(iii) Along BX, mark off points , such that .
(iv) Join .
(v) From draw meeting produced part of BC at C.
(vi) From C’, draw C’ A’  C A intersecting the extended line segment BA at A’.
Thus, A’B’C’ is the required triangle each of whose sides is 3/2 times the corresponding sides of the triangle ABC.