Question

Circles with centres, A, B & C
touch each other externally. If
AB=36.BC = 32,CA =30. then find
the radii of each circle .​

Answer 1

AB=r1+r2=36.

BC=r2+r3=32.

CA=r3+r1=30.

NOW,

AB+CA+BC=2(r1+r2+r3).

ADDING ,

36+30+32=98

THEREFORE, DIVIDE IT BY 2 ,

98÷2= 49.

TO FIND r1,

1》r1+r2+r3=49

r1+32=49-32-------------》(ADDING r2+r3)

》r1=17

2》TO FIND r2,

r1+r2+r3=49

r2+30=49 -------------》(ADDING r1+r3).

r2=49-30

r2=19

3》TO FIND r3,

r1+r2+r3=49

r3+36=49-------------》(ADDING r2+r1)

r3=49-36

r3=13

Therefore,

r1=17

r2=19

r3=13.

VERIFICATION,

r1+r2= 17+19=36.

r2+r3=19+13=32.

r3+r1=13+17=30.

HOPE IT HELPS.