MathDB

Let

AB

be the diameter of a circle with a center

O

and radius

1

. Let

C

and

D

be two points on the circle such that

AC

and

BD

intersect at a point

Q

situated inside of the circle, and \angle AQB\equal{} 2 \angle COD. Let

P

be a point that intersects the tangents to the circle that pass through the points

C

and

D

. Determine the length of segment

OP

Problem Statement