MathDB

acute triangle

Source: 2004 China Second Round Olympiad

August 30, 2014

Pythagorean Theoremgeometrygeometry unsolved

Problem Statement

In an acute triangle

ABC

, point

H

is the intersection point of altitude

CE

to

AB

and altitude

BD

to

AC

. A circle with

DE

as its diameter intersects

AB

and

AC

at

F

and

BE=7

, respectively.

FG

and

AH

intersect at point

K

. If

BC=25

,

BD=20

, and

BE=7

, find the length of

AK

.

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