Circle Quiz 1

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle POB=115^\circ,$ then $\angle APO$ is

In the given figure, find the value of $x^\circ.$

From the given figure, find the value of $x^\circ+y^\circ.$

PA is a tangent to the circle with centre O.

If BC = 3 cm, AC = 4 cm and $\Delta ACB\sim\Delta PAO,$ then OA is equal to

In the given figure, if $\angle ACB=50^\circ,$ then $\angle ATO$ is

In adjoining figure, PQ and PR are tangents to the circle with centre O and S is a point on the circle such that $\angle SQL=50^\circ\;and\;\angle SRM=60^\circ.$ Then $\angle QSR$

In given figure, AB is diameter of a circle with centre O and AT is tangent. If $\angle AOQ=58^\circ,$ then $\angle ATQ=$

In figure, $\angle AOB=125^\circ,$ then $\angle COD$ is equal to

In the given figure, if TP and TQ are tangents to a circle with centre O, so that $\angle POQ=110^\circ,$ then $\angle PTQ$ is

In the given figure, 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, 'O' is the centre of circle, PQ is a chord and the tangent PR at P makes an angle of $50^\circ$ wih PQ, then $\angle POQ$ is equal to:

If two tangents inclined at an angle $60^\circ$ are drawn to a circle of radius 3 cm, then the length of each tangent is equal to:

In the given figure, 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:

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is:

In figure, QR is common tangent to the given circles, touching externally at the point T. The tangent at T meets QR at P. If PT = 3.8 cm, then the length of QR (in cm) is: