Circles — Class 10 Mathematics (Standard) PYQs

In the given figure, PQ is tangent to the circle with centre O. S is a point on the circle such that $\angle SQT=55^{\circ }$. The $m\angle QPS$ is

PQ and PR are two tangents to a circle with centre O and radius $5\text{cm}$. AB is another tangent to the circle at C which lies on OP. If $OP=13\text{cm}$, then find the length $AB$ and $PA$.

PQ is tangent to a circle with centre O. If $OQ = a$, $OP = a + 2$ and $PQ = 2b$, then relation between $a$ and $b$ is

The tangents drawn at the extremities of the diameter of a circle are always :

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 equal to :

A person is standing at P outside a circular ground at a distance of $26\text{m}$ from the centre of the ground. He found that his distances from the points A and B on the ground are $10\text{m}$ (PA and PB are tangents to the circle). Find the radius of the circular ground.

(a) In the given figure, O is the centre of the circle and BCD is tangent to it at C. Prove that $\angle BAC+\angle ACD=90^{\circ }$.
OR
(b) Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

If the length of a chord of a circle is equal to its radius, then the angle subtended by chord at the centre is :

In the given figure, RS is the tangent to the circle at the point L and MN is the diameter. If $\angle NML=30^{\circ }$, then $\angle RLM$ is :

At point A on the diameter AB of a circle of radius $10\text{cm}$, tangent XAY is drawn to the circle. Find the length of the chord CD parallel to XY at a distance of $16\text{cm}$ from A.