MathDB

A circle

\omega

with center

O

and radius

r

is constructed. A point

P

is chosen on the circumference

\omega

and a point A is taken inside it, such that is outside the line that passes through

P

and

O

. Point

B

is constructed, the reflection of

A

wrt

O

. and

P'

is another point on the circumference such that the chord

PP'

is perpendicular to

PA

. Let

Q

be the point on the line

PP'

that minimizes the sum of distances from

A

Q

and from

Q

B

. Show that the value of the sum of the lengths

AQ+QB

does not depend on the choice of points

P

A

Problem Statement