MathDB

The tangent lines to the circle

\omega

at points

B

and

D

intersect at point

P

. The line passing through

P

cuts out from circle chord

AC

. Through an arbitrary point on the segment

AC

a straight line parallel to

BD

is drawn. Prove that it divides the lengths of polygonal

ABC

and

ADC

in the same ratio.
[hide=last sentence was in Russian: ]Докажите, что она делит длины ломаных ABC и ADC в одинаковых отношениях.

Problem Statement