MathDB

exradii problem (2017 Adygea Teachers' Geometry Olympiad p2 RU)

Source:

June 21, 2020

geometryexcircleexradiusexradii

Problem Statement

It turned out for some triangle with sides

a, b

and

c

, that a circle of radius

r = \frac{a+b+c}{2}

touches side

c

and extensions of sides

a

and

b

. Prove that a circle of radius

\frac{a+c-b}{2}

is tangent to

a

and the extensions of

b

and

c