MathDB

2021 Geo #9: Another trapezoid

Source:

May 30, 2021

geometrytrapezoid

Problem Statement

Let

ABCD

be a trapezoid with

AB \parallel CD

and

AD = BD

. Let

M

be the midpoint of

AB,

and let

P \neq C

be the second intersection of the circumcircle of

\triangle BCD

and the diagonal

AC.

Suppose that

BC = 27, CD = 25,

and

AP = 10.

If

MP = \tfrac {a}{b}

for relatively prime positive integers

a

and

b,

compute

100a + b

.

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