Question

PQ and QR are two equal chords of a circle. A diameter of the circle is drawn through Q . Prove that the diameter bisects ∠ PQR.

Answer 1

Let QT be the diameter of ∠ PQR 

Since , PQ = QR

∴ OM = ON

In Δ OMQ and Δ ONQ

OM = ON  (equal chords are equidistant from the centre)

∠ OMQ = ∠ ONQ (90 ° each)

OQ = OQ  (common)

Δ OMQ ≅  Δ ONQ   (RHS)

∴ ∠ OQM = ∠ OQN   (CPCT)

Thus QT i.e. diameter of the circle visects ∠ PQR.