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Geometry - Circles and Tangents

Multiple Choice Questions

1.
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

13 cm

In $increment PAB$ ,
$PB equals space space square root of 6 squared plus 8 squared end root space equals space square root of 36 plus 64 end root space equals space square root of 100 space equals space 10 space cm$
$because$ $increment PAB$ and $increment BCQ$ are similar,
$therefore$ $BC over QC space equals space AB over PA space rightwards double arrow space space space BC over 3 space equals space 8 over 6$
$therefore$ BC = 4 cm
Now, in $increment BCQ$ ,
$BQ space equals space square root of 4 squared plus 3 squared end root space equals space square root of 16 plus 9 end root space equals space square root of 25 space equals space 5 space cm$
$therefore$ PQ = 10 + 5 = 15 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

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°

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