Question

In the adjoining figure, OPQR is a square. A circle drawn with centre O cuts the square at X and Y. Prove that QX = QY.

Answer 1

Given: OPQR is a square. A circle with centre O cuts the square at X and Y.
To prove: QX = QY
Construction: Join OX and OY.

Proof:
In ΔOXP and ΔOYR, we have:
∠OPX = ∠ORY (90° each)
OX = OY (Radii of a circle)
OP = OR (Sides of a square)
∴ ΔOXP ≅ ΔOYR (BY RHS congruency rule)
⇒ PX = RY (By CPCT)
⇒ PQ - PX = QR - RY (PQ and QR are sides of a square)
⇒ QX = QY
Hence, proved.