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In Fig. 7, tangents PQ and PR are drawn from an external point P to a circle with centre O, such that ∠RPQ = 30°. A chord RS is drawn parallel to the tangent PQ. Find ∠RQS.
Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of ∠ L APB is
Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.
In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB = 50°. Write the measure of ∠OAB.
A chord of a circle of radius 10 em subtends a right angle at its centre. The length of the chord (in em) is
`(A) 5sqrt 2`
`(B) 10 sqrt2`
`(D) 10sqrt 3`
From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.
Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y). Find the values of y. Hence find the radius of the circle.