MathDB

BMT 2014 Spring - Geometry P1

Source:

December 29, 2021

geometry

Problem Statement

Let

ABC

be a triangle. Let

r

denote the inradius of

\vartriangle ABC

. Let

r_a

denote the

A

-exradius of

\vartriangle ABC

. Note that the

A

-excircle of

\vartriangle ABC

is the circle that is tangent to segment

BC

, the extension of ray

AB

beyond

B

and the extension of

AC

beyond

C

. The

A

-exradius is the radius of the

A

-excircle. Define

r_b

and

r_c

analogously. Prove that

\frac{1}{r}=\frac{1}{r_a}+\frac{1}{r_b}+\frac{1}{r_c}

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