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

In the given figure, find the value of $x^{\circ }\mathrm{.}x^\backslash circ.$

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

PA is a tangent to the circle with centre O.

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

In the given figure, if $\mathrm{\angle }ACB=50^{\circ },\backslash angle\; ACB=50^\backslash circ,$ then $\mathrm{\angle }ATO\backslash angle\; ATO$ 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 $\mathrm{\angle }SQL=50^{\circ }and\mathrm{\angle }SRM=60^{\circ }\mathrm{.}\backslash angle\; SQL=50^\backslash circ\backslash ;and\backslash ;\backslash angle\; SRM=60^\backslash circ.$ Then $\mathrm{\angle }QSR\backslash angle\; QSR$

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

In figure, $\mathrm{\angle }AOB=125^{\circ },\backslash angle\; AOB=125^\backslash circ,$ then $\mathrm{\angle }COD\backslash angle\; COD$ is equal to

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

In the given figure, AT is a tangent to the circle with centre 'O' such that OT = 4 cm and $\mathrm{\angle }OTA=30^{\circ }\mathrm{.}\backslash angle\; OTA=30^\backslash circ.$ 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 $50^{\circ }50^\backslash circ$ wih PQ, then $\mathrm{\angle }POQ\backslash angle\; POQ$ is equal to:

If two tangents inclined at an angle $60^{\circ }60^\backslash circ$ 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 $\mathrm{\angle }ACB=50^{\circ }\mathrm{.}\backslash angle\; ACB=50^\backslash circ.$ If AT is the tangent to the circle at the point A, then $\mathrm{\angle }BAT\backslash angle\; BAT$ 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: