Construction: Join OX and OY

In Δ OPX and ΔORY,

OX = OY (radii of the same circle)

OP = OR (sides of the square)

∴ΔOPX Δ ORY (RHS rule)

∴ PX = RY (CPCT)—1

OPQR is a square

∴ PQ = RQ

∴ PX + QX = RY + QY

QX = QY (from –1)

Hence proved