Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

Solve any two sub-question:

Prove that, “The lengths of the two tangent segments to a circle drawn from an external point are equal.”

In fig 3.28 the circles with centres A and B touch each other at E. Line is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii Fig. 3.28 of the circles are 4 cm, 6 cm.

In figure 3.80, if PQ = 6, QR = 10, PS = 8 find TS.

In figure 3.79, O is the centre of the circle and B is a point of contact. seg OE seg AD, AB = 12, AC = 8, find

(1) AD

(2) DC

(3) DE.

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

Two circles of radii 5.5 cm and 3.3 cm respectively touch each other. What is the distance between their centers?

In figure 3.81, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DE × GE = 4r²

If radii of two circles are 4 cm and 2.8 cm. Draw figure of these circles touching each other –

(i) externally

(ii) internally.

Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.

In fig 3.27, the circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively. Prove that -

(1) seg AP || seg BQ,

(2) ∆ APR ~ ∆ RQB, and

(3) Find ∠ RQB if ∠ PAR = 35°