MathDB

2018 JHMT Geometry #10

Source:

September 5, 2023

geometry

Problem Statement

In an acute triangle

ABC

, the altitude from

C

intersects

AB

at

E

and the altitude from

B

intersects

AC

at

D

.

CE

and

BD

intersect at a point

H

. A circle with diameter

DE

intersects

AB

and

AC

at points

F,G

respectively.

FG

and

AH

intersect at

K

. If

\overline{BC} = 25

,

\overline{BD} = 20

, and

\overline{BE} = 7

, the length of

AK

is of the form

\frac{p}{q}

, where

p, q

are relatively prime positive integers. Find

p + q

.

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