Question

Circles with centres A, B, and C touch each other externally. If AB = 3cm, BC = 3 cm CA = 4 cm, then find the radii of each circle.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The radii of each circle are A = C = 2 cm and B = 1 cm.

Given,

Circles with centers A, B, and C touch each other externally.

AB = 3cm, BC = 3 cm CA = 4 cm

Let "a" be the radius of circle with center A.

Let "b" be the radius of circle with center B .

Let "c" be the radius of circle with center C.

From figure, it's clear that,

a + b = 3 cm .......(1)

b + c = 3 cm ........(2)

c + a = 4 cm ..........(3)

(1) - (2) gives,

a - c = 3 cm ...........(4)

(3) + (4) gives,

2a = 4

a = 2 cm

from (3)

c = 4 - a

c = 4 - 2

c = 2 cm

from (2)

b = 3 - c

b = 3 - 2

b = 1 cm.

Therefore, the radius of circle with center A is = a = 2 cm.

the radius of circle with center B is = b = 1 cm.

the radius of circle with center C is = c = 2 cm.