Awesome geometry -4

Geometry Level 4

In a right angled triangle A B C \triangle ABC with C = 9 0 \angle C=90^\circ with r + r A + r B = r C = 35 r + r_A + r_B = r_C = 35 .

Find the perimeter of A B C \triangle ABC .

Details and Assumptions :

  • r r is inradius.

  • r A , r B , r C r_A , r_B , r_C are radii of excircles opposite to vertices A , B , C A,B,C .


The answer is 70.

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3 solutions

Aryan Goyat
Feb 20, 2016

semiperimeter=Rc we simply use the fact that excenter lie on internal angle bisector of C and use a little geometry.

Ritwik Kadu
Feb 16, 2016

The first part is/was unnecessary. rc=0 was enough

Ronak Agarwal
Apr 22, 2015

Well it must be mentioned that it is right angled at C.

Anyways in a right triangle.

s ( s c ) = Δ s(s-c)= \Delta where s is the semi permeter.

Also r c = Δ s a r_{c}=\frac{\Delta}{s-a}

Rest is self explanatory.

Actually , I had mentioned that earlier. But someone from the moderators has edited this question.

Nihar Mahajan - 6 years, 1 month ago

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