MathDB

Right Triangle and Circles

Source:

December 28, 2006

geometryinradiusincenteranalytic geometrysimilar triangles

Problem Statement

Let

\triangle{PQR}

be a right triangle with

PQ=90

,

PR=120

, and

QR=150

. Let

C_{1}

be the inscribed circle. Construct

\overline{ST}

with

S

on

\overline{PR}

and

T

on

\overline{QR}

, such that

\overline{ST}

is perpendicular to

\overline{PR}

and tangent to

C_{1}

. Construct

\overline{UV}

with

U

on

\overline{PQ}

and

V

on

\overline{QR}

such that

\overline{UV}

is perpendicular to

\overline{PQ}

and tangent to

C_{1}

. Let

C_{2}

be the inscribed circle of

\triangle{RST}

and

C_{3}

the inscribed circle of

\triangle{QUV}

. The distance between the centers of

C_{2}

and

C_{3}

can be written as

\sqrt{10n}

. What is

n

?

Back to Problems View on AoPS