Circles: 2 marks Questions (CBSE Class 10)

In the given figure, AP, AQ and BC are tangents to the circle with centre O. If AB = 6 cm, AC = 7 cm and BC = 5 cm, then what is the length of AP ?

In the given figure, TP is tangent to a circle with centre O. Diameter BA when produced meets the tangent at T. If $\angle$ ABP = $35^{\circ }$, then find the measure of $\angle$ PTA.

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

In the given figure, a circle with centre O is inscribed inside $△LMN$. A and B are the points of tangency. Find $\angle ANB$.

In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.

Two concentric circles are of radii 6 cm and 10 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Prove that the tangent drawn at any point of the circle is perpendicular to the radius through the point of contact.

A quadrilateral circumscribes the circle as shown in the given figure. If AB = 5 cm, BC = 7 cm and CD = 6 cm, then find the length of AD.

In the given figure, $△ABC$ circumscribes a circle. If AR = 3 cm, BP = 4 cm and QC = 5 cm, find the perimeter of $△ABC$.

In the given figure, TP and TQ are two tangents. If $\angle PTQ=50^{\circ }$, then find the measure of $\angle OPQ$.

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

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

Prove that the tangents drawn at the ends of a diameter of a circle are parallel to each other.

XY and PQ are two tangents drawn at the end points of the diameter AB of a circle. Prove that $XY\parallel PQ$.

The length of a tangent drawn to a circle from a point A, at a distance of 10 cm from the centre of the circle, is 6 cm. Find the radius of the circle.

In the given figure, AB and CD are tangents to a circle centred at O. Is $\angle BAC=\angle DCA$ ? Justify your answer.

In the given figure, O is the centre of the circle. If $\angle AOB=145^{\circ }$, then find the value of x.

In the given figure, $△ABC$ is circumscribing a circle. Find the length of BC, if AR = 4 cm, BR = 3 cm and AC = 11 cm.

If two tangents inclined at an angle of $60^{\circ }$ are drawn to a circle of radius 3 cm, then find the length of each tangent.

In the adjoining figure, PT is a tangent at T to the circle with centre O. If $\angle TPO=30^{\circ }$, find the value of $x$.

PA and PB are tangents drawn to the circle with centre O as shown in the figure.
Prove that $\angle APB=2\angle OAB$.

In the given figure, tangents AB and AC are drawn to a circle centred at O. If $\angle OAB=60^{\circ }$ and OB = 5 cm, find lengths OA and AC.

From a point P, the length of the tangent to a circle is 24 cm and the distance of P from the centre of the circle is 25 cm. Find the radius of the circle.

In the given figure, O is the centre of the circle. AB and AC are tangents drawn to the circle from point A. If $\angle BAC=65^{\circ }$, then find the measure of $\angle BOC$.

In the given figure, PT is a tangent to the circle centered at O. OC is perpendicular to chord AB. Prove that $PA\cdot PB=P{C}^2-A{C}^2$.

In the given figure, PQ is a chord of the circle centered at O. PT is a tangent to the circle at P. If $\angle QPT=55^{\circ }$, then find $\angle PRQ$.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

In the given figure, PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If $\angle AOC=130^{\circ }$, then find the measure of $\angle APB$, where O is the centre of the circle.

In Figure 1, if tangents PA and PB drawn from a point P to a circle with centre O, are inclined to each other at an angle of $70^{\circ }$, then find the measure of $\angle POA$.

In Fig. 1, perimeter of $△PQR$ is 20 cm. Find the length of tangent PA.

In Fig. 2, BC is tangent to the circle at point B of circle centred at O. BD is a chord of the circle so that $\angle BAD=55^{\circ }$. Find m$\angle DBC$.

In Figure 2, PA and PB are tangents to the circle with centre at O. If $\angle APB=70^{\circ }$, then find m$\angle AQB$.

In Figure 1, PA and PB are tangents to the circle with centre at O. If $\angle APB=70^{\circ }$, then find m$\angle AQB$.

The distance between two tangents parallel to each other of a circle is 13 cm. Find the radius of the circle.

Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

In Fig. 1, AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and $\angle AOP=60^{\circ }$, then find m$\angle C$.

In Fig. 2, XAY is a tangent to the circle centered at O. If $\angle ABO=40^{\circ }$, then find m$\angle BAY$ and m$\angle AOB$.

In Figure 2, PQ and PR are tangents to the circle centred at O. If $\angle$ OPR = $45^{\circ }$, then prove that ORPQ is a square.

In Figure 1, PQ and PR are tangents to the circle centred at O. If $\angle$ OPR = $45^{\circ }$, then prove that ORPQ is a square.

In Fig. 1, there are two concentric circles with centre O. If ARC and AQB are tangents to the smaller circle from the point A lying on the larger circle, find the length of AC, if AQ = 5 cm.