MathDB

In an acute triangle

ABC

, a point

P

is taken on the

A

-altitude. Lines

BP

and

CP

intersect the sides

AC

and

AB

at points

D

and

E

, respectively. Tangents drawn from points

D

and

E

to the circumcircle of triangle

BPC

are tangent to it at points

K

and

L

, respectively, which are in the interior of triangle

ABC

. Line

KD

intersects the circumcircle of triangle

AKC

at point

M

for the second time, and line

LE

intersects the circumcircle of triangle

ALB

at point

N

for the second time. Prove that

\frac{KD}{MD}=\frac{LE}{NE} \iff \text{Point P is the orthocenter of triangle ABC}

Problem Statement