MathDB

2013 HMMT Guts #19: Circumscribed Triangles

Source:

March 26, 2013

HMMTgeometrytrapezoidsimilar triangles

Problem Statement

An isosceles trapezoid

ABCD

with bases

AB

and

CD

has

AB=13

,

CD=17

, and height

3

. Let

E

be the intersection of

AC

and

BD

. Circles

\Omega

and

\omega

are circumscribed about triangles

ABE

and

CDE

. Compute the sum of the radii of

\Omega

and

\omega

.

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