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computational geo with arc midpoint

Source: 2023 Portugal p2 OPM

March 26, 2024

geometryarc midpoint

Problem Statement

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}

.

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