Question

PQ and PR are tangents to the circle centred at O. If OPR = 45°, then prove that ORPQ is a square.

Answer 1

OPR is 1/2 QPR
The tangents are perpendicular to the radii.

Answer 2

Ang OPR = 1/2 Ang RPQ
Hence, Ang RPQ = 90°
Ang QOR = 90° ( Supplementary angles in a cyclic quadrilateral )

Also, Ang OQP = Ang ORP = 90° ( radii perpendicular to tangents)

Hence, we can say ORPQ is a square.

Answer 3

Ans