Difference between revisions of "1964 IMO Problems/Problem 3"

(Created page with '== Problem == A circle is inscribed in a triangle <math>ABC</math> with sides <math>a,b,c</math>. Tangents to the circle parallel to the sides of the triangle are contructed. Eac…')
 
(Solution)
Line 3: Line 3:
  
 
== Solution ==
 
== Solution ==
 +
{{solution}}

Revision as of 11:38, 16 July 2009

Problem

A circle is inscribed in a triangle $ABC$ with sides $a,b,c$. Tangents to the circle parallel to the sides of the triangle are contructed. Each of these tangents cuts off a triangle from $\triangle ABC$. In each of these triangles, a circle is inscribed. Find the sum of the areas of all four inscribed circles (in terms of $a,b,c$).

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Invalid username
Login to AoPS