In 4ABC, altitude AD = 24, inradius of 4ABD = 3 and
inradius of 4ACD = 6. Find BC.

Question

In 4ABC, altitude AD = 24, inradius of 4ABD = 3 and inradius of 4ACD = 6. Find BC.

Badiuddin askIITians.ismu Expert · Answer

Dear ajinkya

tanB = AD/BD = 24/BD

tanB/2 = r1/(BD-r1)

tanB = 2tanB/2 /( 1 - tan²B/2)

24/BD = 2 {r1/(BD-r1)}/ 1- { r1/(BD-r1)}²

BD = (24r1 -r1² )/(12-r1)

r1 =3

BD = 7

similerly

CD = 18

BC = 7+18 = 25

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In 4ABC, altitude AD = 24, inradius of 4ABD = 3 and inradius of 4ACD = 6. Find BC.

In 4ABC, altitude AD = 24, inradius of 4ABD = 3 and
inradius of 4ACD = 6. Find BC.

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