10 Question MCQ (including Assertion)

If angle between two radii of a circle is \(130^\circ\), the angle between the tangents at the ends of the radii is:

In Fig. 9.1, the pair of tangents AP and AQ drawn from an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is

If tangents PA and PB drawn from an external point P to the circle with centre O are inclined to each other at an angle of \(80^{\circ}\) as shown in the given figure, then the measure of \(\angle \mathrm{POA}\) is :

Maximum number of common tangents that can be drawn to two circles intersecting at two distinct points is :

From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is

Assertion (A) : If two tangents are drawn to a circle from an external point, then they subtend equal angles at the centre of the circle.
Reason (R) : A parallelogram circumscribing a circle is a rhombus.

In Fig. 9.4, AB is a chord of the circle and AOC is its diameter such that \(\angle ACB=50^\circ\). If AT is the tangent to the circle at the point A, then \(\angle BAT\) is equal to

In Fig. 9.5, AT is a tangent to the circle with centre O such that OT = 4 cm and \(\angle OTA=30^\circ\). Then AT is equal to

In the given figure, PA is a tangent to a circle with centre O . If \(\mathrm{OP}=10 \mathrm{~cm}\), then the length of AP is :