### Mathematics Class X

Real Numbers
Polynomials
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Circles
Constructions
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

# Construction of a Triangle similar to a given Triangle as per given Scale

The scale factor is the ratio of the sides of the triangle given to the sides of the triangle to be made by the steps of construction.

Example:

Draw a triangle similar to ABC with its sides equal to of the corresponding sides of the given triangle ABC. (Scale factor = ).

Steps of Construction

Step 1: Draw a line AX by making an acute angle with the line segment AB.

Step 2: Mark three points of equal size using a compass on the line AX. Points will be depending upon the scale factor as we have to mark the number of points which is greater in the scale factor. In the ratio of .

Step 3: Join BX3 and draw a line from X2 parallel to BX3 to intersect AB at P.

Step 4: Draw a line parallel to BC from point P to intersect AC at Q.

Now .

##### Construction of Tangents to a Circle

Tangent is a line which intersects the circle at one point only at the outer of the circle. It is always perpendicular to the radius of the circle.

Example:

Construct the pair of tangents to the circle of radius 3 cm from the point which is 7 cm away from its centre, and measure their lengths also.

Steps of Construction

Step 1: Draw a circle of radius 3 cm by taking O as the centre.

Step 2: Mark a point P outside the circle at a distance of 7 cm from the centre O. Join OP.

Step 3: Bisect the line segment OP, so that the perpendicular bisector of OP intersects it at the point M.

Step 4: Now draw another circle by taking M as centre and MO as radius, which intersects the given circle at two points’ i.e. T and Tꞌ.

Step 5: Now join PT and PTꞌ which are the required tangents and measure the length of the tangents.

The length of the tangents is PT = PTꞌ = 6.3 cm.

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