# Ratios Involving Six Radii

Ratios Involving Six Radii

Given a point on the side of the triangle , let and be the radii of the inscribed circles of the triangles and , and let and be the radii of the circumcircles of the triangles and . Let and denote the radii of the inscribed circle and the circumcircle of the triangle , respectively. Prove that =.

M

AB

ABC

r

1

r

2

ACM

BCM

ρ

1

ρ

2

ACM

BCM

r

ρ

ABC

rr

1

2

ρρ

1

2

r

ρ