A small and interesting problem.

Level pending

In a triangle ABC which holds : r1 =r2 + r3 +r

where r1 , r2 , r3 are the exradii of the triangle and 'r' is the inradius. The triangle is a :

1.) Isoceles triangle

2.) Scalene triangle

3.) Rightangled triangle

4.) Equilateral triangle

2 4 1 3

1 solution

Gaurav Jain
May 15, 2015

We use a simple result : r1 + r2 + r3 =4R +r. hence, r1= 2R + r. Now , $\frac { \triangle }{ (s-a) } -\frac { \triangle }{ (s) } =\frac { abc }{ 2\triangle }$

There fore ${ b }^{ 2 }+{ c }^{ 2 }={ a }^{ 2 }$ Hence a right angled triangle.

A small and interesting problem.

1 solution

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