Tangents and Radii

How many tangents to a circle passing

through a point lying inside the circle

• One

• 2

• Zero

• Infinite

In the given figure, AB and AC are tangents to the circle with centre O such that angle BAC = 40° , then angle BOC is equal to

• 40°

• 50°

• 140°

• 150°

In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm.Then the radius of the circle is

• 25 cm

• 26 cm

• 24 cm

• 10 cm

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

• 60 sq cm

• 65 sq cm

• 30 sq cm

• 32.5 sq cm

In the given figure, if O is the centre of circle PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then angle POQ is equal to

• 100°

• 80°

• 90°

• 75°

In figure AP and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA is perpendicular to PB, then the length of each tangent is

• 3 cm

• 4 cm

• 5 cm

• 6 cm

In figure, if angle ATO = 40°, find angle AOB

• 120°

• 140°

• 100°

• 80°

In figure CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R, if CP = 11 cm and BC = 7 cm, then the length of BR is

• 18 cm

• 4 cm

• 9 cm

• 15 cm

Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of larger circle which touches the smaller circle is

A tangent PQ of a circle of radius 7 cm meets a line through centre O at a point Q so that OQ = 25 cm, then the length of PQ is