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A chord AB of a circle lies at 9 cm from the centre 0. The radius of the circle is 15 cm. What is the length of the chord?
Let the midpoint of AB be C. Use Pythagoras theorem to calculate the length of CB.
(1)
Length of the chord AB is 24 cm.
Given the PQ, QR and RS are the chords of a circle. PQ and RS both are perpendicular to QR. Which of the following is correct?
If we join PR and QS, both will be the diameters of the circle and they will same length and therefore PQ and RS are also equal in length.
In the following figure PQ and PR are the chords of a circle such that PQ = PR = 8 cm. The circle has a radius of 5 cm and centre O. Point S is the midpoint of QR. What is the length of OS?
(1)
Subtract the equations
(2)
Angles subtended by the chords PR and PQ at the centre of a circle O are 58° and 122° respectively. What is the measure of the angle PRQ?
(1)
ABCD is a cyclic quadrilateral with angle DCB as 40° and angle BAC as 60°. What is the measure of the angle CAD?
Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
AB is a chord of the circle with centre O. What is the measure of \(b + c\)?
Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
What is the value of \(k\) in the following figure?
Angle in a semicircle is a right angle. Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
PQRS and TQRS are cyclic quadrilaterals in the following figure. What is the measure of the angle STQ?
Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
What is the value of \(k\) in the following figure?
Plot a point S anywhere on the major arc PQ. Join PS and QS. The angle PSR will be half of the angle POR. Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
The length of a chord of a circle is equal to the radius. What is the measure of the angle subtended by this chord at the centre of the circle?
The triangle formed will be an equilateral triangle. Therefore, the angle subtended by this chord at the centre of the circle is 60°.
What is the value of \(k\) in the following figure?
Plot a point S anywhere on the major arc PQ. Join PS and QS. The angle PSR will be half of the angle POR. Sum of opposite angles of a cyclic quadrilateral is 180°.
(1)
The length of PR and PQ in the following diagram are 20 cm and \(10\sqrt{3}\) cm. Find the length of PQ.
Triangle drawn in a semicircle is a right triangle.
(1)
Length of PQ is 10 cm.
The lengths of two chords PQ and RS of a circle are 12 cm and 16 cm respectively. They lie on the opposite sides of the centre of the circle. If PQ lies at a distance of 8 cm from the centre then find the distance between the chord RS and centre of the circle.
Let the midpoints of PQ and RS be A and B respectively.
(1)
The distance between the chord RS and the centre of circle O is 6 cm.
The lengths of two chords PQ and RS of a circle are 20 cm and 44 cm respectively. They lie on the opposite sides of the centre of the circle. If the distance between the chords is 24 cm then find the radius of the circle.
Let the midpoints of PQ and RS be A and B respectively. Let , therefore
(1)
Subtracting the equations, we get
(2)
ADBO and ABCO are parallelograms and DBC is a straight line. What is the measure of the angle DAC?
The sides of both the parallelograms are equal to the radius. The triangle DAB and BOA are equilateral triangles. Therefore, . The triangles BAC and OAC are congruent to each other. Therefore, .
(1)