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Square Inscribed in Sector

Source: 2004 IrMO Paper 1 Problem 3

December 28, 2017

vectorgeometry

Problem Statement

AB

is a chord of length

6

of a circle centred at

O

and of radius

5

. Let

PQRS

denote the square inscribed in the sector

OAB

such that

P

is on the radius

OA

,

S

is on the radius

OB

and

Q

and

R

are points on the arc of the circle between

A

and

B

. Find the area of

PQRS

.

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