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.

View wiki
Nihar Mahajan by Nihar Mahajan , 20, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

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.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Ritwik Kadu
Feb 16, 2016

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

0 Helpful 0 Interesting 0 Brilliant 0 Confused
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.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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

Nihar Mahajan - 6 years, 1 month ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...