2

Part of 2023 Portugal MO

Problems(1)

computational geo with arc midpoint

Source: 2023 Portugal p2 OPM

3/26/2024

Let

[AB]

be a diameter of a circle with center

O

and radius

1

. Consider

P

a point on the circumference, different from

A

and

B

and let

Q

be the midpoint of the arc

AP

. The line parallel to

PQ

that passes through

O

intersects the line

PB

at point

S

. Determine

\overline{PS}

.

geometryarc midpoint