MathDB

Regional Olympiad - FBH 2018 Grade 10 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

September 18, 2018

geometrycircumcircleperpendicular bisector

Problem Statement

Let

P

be a point on circumcircle of triangle

ABC

on arc

\stackrel{\frown}{BC}

which does not contain point

A

. Let lines

AB

and

CP

intersect at point

E

, and lines

AC

and

BP

intersect at

F

. If perpendicular bisector of side

AB

intersects

AC

in point

K

, and perpendicular bisector of side

AC

intersects side

AB

in point

J

, prove that:

{\left(\frac{CE}{BF}\right)}^2=\frac{AJ\cdot JE}{AK \cdot KF}