Circles Test - ...

In the given circle, O is the centre, AB = BC and OM = 5 units. The length of ON is equal to ____.

In the given figure, AB and AC are two tangents to a circle with centre O.



What is the perimeter of the figure OCAB, if AB = 7 cm and OC = 3 cm?

In the given figure, AB is the diameter of the circle and points C and D are on the circumference, such that = 30° and = 70°. What is the measure of ?

In the given figure, O is the centre of the circle, RPM = 30° and TPN = 60°. Then find the measure of PMN.

In the given figure, if PM and PN are tangents to the circle with centre Q, radius = 7 cm and PM = 7 cm, then what is the length of PQ?

In the given figure, O is the centre of the circle. What is the measure of BDC?

In the figure (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T, such that CT becomes a tangent to the circle at point C. If ATC = 30° and ACT = 50°, find the measure of angle ∠BOA.

In the figure given below, AB is a diameter of the circle, TD is a tangent to the circle and AB = 2AD. If AHD = 36° and DBA = 30°, then what is the measure of CDT?

In a circle of radius 'a' and centre 'O', an isosceles triangle ABC is inscribed as shown below. Then the length of the equal side of the triangle is

In the given figure, O is the centre of the circle and PQ is a tangent to the circle at P.


If OP = 3 cm and PQ = 12 cm, then what is the length of OQ?

PA and PB are two tangents to a circle with centre O. If chord AB intersects OP at a point R, then which of the following relations is true?

From an external point A, AB and AC are two tangents drawn to a circle with centre O. If BAC : BOC = 2 : 3, what is the measure of BOC?

In the figure given below (not drawn to scale), A, B and C are three points on a circle with centre O. The chord BA is extended to a point T such that CT becomes tangent to the circle at point C. If = 30° and = 50°, then measures

From a point P, a tangent is drawn to a circle. If the length of the tangent is 3 cm and the distance of point P from the centre of the circle is 5 cm, find the radius of the circle.

In the given figure, if POS = x°, ROQ = y°, POQ = a°, ROS = b°, PS = RQ and RS = PQ, then which of the following relations is definitely true?

The number of tangents drawn from a point outside a circle is

PA and PB are two tangents to a circle with centre O. If AOP : OPB = 13 : 5, find the measure of OPA.

Two circles 'a' and 'b' having equal radius 'k' intersect each other in such a way that each circle passes through the centre of the other circle. What is the ratio of the length of the common chord to the total circumference of both the circles?

In the given figure, OTQ = 36°, what is the measure of TPQ?

Using the given figure, find the following:

(i) SNR
(ii) SPQ

In the given figure, ∠DBC = 38° and O is the centre of the circle. Find the measure of angle x.

The length of a chord QR is 16 cm and tangents QT and RT are 17 cm long. Find the diameter of the circle if the distance of point T from the centre of the circle is 21 cm.

Match the columns.

Column I	Column II
(a) In the given figure, O is the centre of the circle and tangent PQ touches the circle at point P. PQ = 8 cm, find the length of the chord AB.	(i) cm
(b) In the given figure, O is the centre of the circle. Tangent XY touches the circle at point Z. Find the length of XZ.	(ii) cm
(c) In the given circle with centre O, YZ is a tangent to the circle which touches the circle at Z. AB is a chord such that area of triangle OAZ = cm2. YZ = 6 cm and OY = 10 cm. Find the length of the chord AB.	(iii) cm

In the following figure, there are two concentric circles. If MN is the radius of the smaller circle and AB is a chord in the bigger circle which touches the smaller circle at N, then what will be the length of AB given that the radii of the two circles are 7.5 cm and 4.5 cm?

The given circle with centre O has three tangents AB, BC and MN. Find the measure of ∠ABC.