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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.

Grade:10

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear ajinkya


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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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