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Question: The radii r<sub>1</sub>, r<sub>2</sub>, r<sub>3</sub> of escribed circles of the triangle ABC are in...

The radii r1, r2, r3 of escribed circles of the triangle ABC are in H.P. If its area is 24 sq. cm and its perimeter is 24 cm, then the lengths of its sides are –

A

4, 6, 8

B

3, 9, 11

C

6, 8, 10

D

None of these

Answer

6, 8, 10

Explanation

Solution

r1, r2, r3 are in H.P. or , , are in A.P.

⇒ s – a, s – b, s – c are in A.P.

⇒ a, b, c, are in A.P.

Now, a + b + c = 24

⇒ b = 8, s = 12, c = 4 – a

or a2 – 16a + 60 = 0

⇒ a = 10, 6

If a = 10, b = 6

If a = 6, b = 10

Sides 6, 8, 10.