MathDB

BP bisects segment DE, projections related (Kharkiv City XI 2019 Ukr)

Source:

March 22, 2020

geometryprojectionsbisects segmentKharkivaltitudes

Problem Statement

In the acute-angled triangle

ABC

, let

CD, AE

be the altitudes. Points

F

and

G

are the projections of

A

and

C

on the line

DE

, respectively,

H

and

K

are the projections of

D

and

E

on the line

AC

, respectively. The lines

HF

and

KG

intersect at point

P

. Prove that line

BP

bisects the segment

DE