10 Question MCQ (including Assertion)

In Fig. 9.7, if PA and PB are tangents to the circle with centre O such that \(\angle APB=50^\circ\), then \(\angle OAB\) is equal to

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. 9.8, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and \(\angle BQR=70^\circ\), then \(\angle AQB\) is equal to

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 :

In the given figure, PT is a tangent to the circle with centre O and radius r . If \(\angle \mathrm{POT}=45^{\circ}\), then the length of OP is :

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 :

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

If PQ and PR are tangents to the circle with centre O and radius 4 cm such that \(\angle \mathrm{QPR}=90^{\circ}\), then the length OP is