Four alternative answers for each of the following questions are given. Choose the correct alternative.

(1) Two circles of radii 5.5 cm and 3.3 cm respectively touch each other. What is the distance between their centers ?
(A) 4.4 cm (B) 8.8 cm (C) 2.2 cm (D) 8.8 or 2.2 cm
Solution:
If the circles touch each other externally, distance between their centres is equal to the sum of their radii.
Distance between the centres = 5.5+3.3 = 8.8cm
The distance between the centres of the circles touching internally is equal to the difference of their radii.
Distance between the centres = 5.5-3.3 = 2.2cm
Hence Option D is the answer.

(2) Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle ?
(A) 6 cm (B) 12 cm (C) 24 cm (D) can’t say
Solution:

Let A and B be centres of two circles.
Then radius of circle with centre A = radius of circle with centre B = Distance between their centres = 12 cm
Hence Option B is the answer.

(3) A circle touches all sides of a parallelogram. So the parallelogram must be a, ………………. .
(A) rectangle (B) rhombus (C) square (D) trapezium
Solution:
It will be a rhombus because rhombus is a parallelogram with all sides equal.
Hence Option B is the answer.

(4) Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.
(A) 25 cm (B) 24 cm (C) 7 cm (D) 14 cm
Solution:

In PQR , Q = 90˚ [Tangent theorem]
PR² = PQ²+QR² [Pythagoras theorem]
12.5² = PQ²+12²
PQ² = 12.5²-12²
PQ² = 156.25-144 = 12.25
PQ = √12.25 = 3.5
Diameter = 2×3.5 = 7cm
Hence Option C is the answer.

(5) If two circles are touching externally, how many common tangents of them can be drawn?
(A) One (B) Two (C) Three (D) Four
Solution:

If two circles touch each other externally, then three common tangents can be drawn to the circles.
Hence Option C is the answer.