Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Geometry - Circles and Tangents

Multiple Choice Questions

AC is transverse common tangent to two circles with centres P and Q and radii 6cm and 3 cm at the point A and C, respectively. If AC cuts PQ at the point B and AB = 8 cm, then the length of PQ is

10 cm
12 cm
13 cm
13 cm

1453 Views

PR is a tangent to a circle with centre O and radius 4 cm at point Q. If $angle POR space equals space 90 degree$ , OR = 5 cm and OP = $20 over 3 cm comma$ then the length of PR is:

3 cm
$16 over 3 cm$
$23 over 3 cm$
$23 over 3 cm$

1019 Views

A chord of a circle is equal to its radius. A tangent is drawn to the circle at an extremity of the chord. The angle between the tangent and the chord is

30°
45°
60°
60°

588 Views

Two circles with centres P and Q touch each other externally. A straight line drawn through the point of contact intersects the circle with centre P at A and the circle with centre Q at B. Then, which of the following is true?

AP = BQ
AP/BQ
AP || BQ
AP || BQ

328 Views

PQ is a tangent to the circle at T. If TR = TS where R and S are points on the circle and ∠RST = 65°, the ∠PTS = ?

65°
130°
115°
115°

1182 Views

In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is

$2 square root of 13 space cm$
$5 square root of 3 space cm$
$4 square root of 6 space cm$
$4 square root of 6 space cm$

1253 Views

Let P and Q be two points on a circle with centre O. If two tangents of the circle through P and Q meet at A with $angle PAQ space equals space 48 degree comma space then space angle APQ$ is

96°
48°
66°
66°

390 Views

8.
AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If $angle CAB space equals space 34 degree$ , then measure of $angle CBA$ is

56°

34°

68°

68°

56°

The angle at the circumference of a semi-circle is always a right angle.
$therefore space space angle ACB space equals space 90 degree space space space space angle CAB space equals space 34 degree therefore space space angle CBA space equals space 90 degree space minus space 34 degree space equals space 56 degree$

585 Views

The radius of a circle is 6 cm. The distance of a point lying outside the circle from the centre is 10 cm. The length of the tangent drawn from the outside point to the circle is

5 cm
6 cm
7 cm
8 cm

333 Views

10.

A, B, C are three points on a circle. The tangent at A meets BC produced at T, $angle BTA space equals space 40 degree comma space space angle CAT space equals 44 degree$ . The angle subtended by BC at the centre of the circle is