MathDB

Let

AOB

be a given angle less than

180^{\circ}

and let

P

be an interior point of the angular region determined by

\angle AOB

. Show, with proof, how to construct, using only ruler and compass, a line segment

CD

passing through

P

such that

C

lies on the way

OA

and

D

lies on the ray

OB

, and

CP:PD=1:2

1