MathDB

Let

AB

and

CD

be two disjoint chords of a circle. A point

E

, distinct from

A

and

B

, is taken on the chord

AB

. Consider the arc

AB

not containing

C

and

D

. Using a ruler and a compass, construct a point

F

on this arc such that \frac{PE}{EQ}\equal{}\frac{1}{2}, where

P

and

Q

are the intersection points of

AB

with the segments

FC

and

FD

, respectively.

Problem Statement