MathDB

Let

ABC

to be an acute triangle. Also, let

K

and

L

to be the two intersections of the perpendicular from

B

with respect to side

AC

with the circle of diameter

AC

, with

K

closer to

B

than

L

. Analogously,

X

and

Y

are the two intersections of the perpendicular from

C

with respect to side

AB

with the circle of diamter

AB

, with

X

closer to

C

than

Y

. Prove that the intersection of

XL

and

KY

lies on

BC

Problem Statement