MathDB

intersection lies on the altitude

Source: JBMO 2000, Problem 3

June 11, 2004

geometrysymmetrycircumcircleangle bisectorprojective geometrycyclic quadrilateral

Problem Statement

A half-circle of diameter

EF

is placed on the side

BC

of a triangle

ABC

and it is tangent to the sides

AB

and

AC

in the points

Q

and

P

respectively. Prove that the intersection point

K

between the lines

EP

and

FQ

lies on the altitude from

A

of the triangle

ABC

. Albania