MathDB

Point of concurrence on the altitude

Source: Iberoamerican 2015 #4

November 11, 2015

geometry

Problem Statement

Let

ABC

be an acute triangle and let

D

be the foot of the perpendicular from

A

to side

BC

. Let

P

be a point on segment

AD

. Lines

K

and

CP

intersect sides

AC

and

AB

at

E

and

F

, respectively. Let

J

and

K

be the feet of the peroendiculars from

E

and

F

to

AD

, respectively. Show that

\frac{FK}{KD}=\frac{EJ}{JD}

.

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