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China TST 1996 diameter circle cut

Source: China TST 1996, problem 1

May 17, 2005

geometrytrapezoidChina

Problem Statement

Let side

BC

of

\bigtriangleup ABC

be the diameter of a semicircle which cuts

AB

and

DG

at

EF

and

E

respectively.

F

and

G

are the feet of the perpendiculars from

D

and

E

to

BC

respectively.

DG

and

EF

intersect at

M

. Prove that

AM \perp BC

.

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