Q20 of 141 Page 464

PQ and RQ are the chords of a circle equidistant from the centre. Prove that the diameter passing through Q bisects ∠PQR and ∠PSR.

Given: chords PQ and RQ are equidistant from center.


Here consider ΔPQS and ΔRQS


Here,


QS = QS (common)


∠QPS = ∠QRS (right angle)


PQ = QS (chords equidistant from center are equal in length)


∴ By RHS congruency ΔPQS ΔRQS


∴ ∠RQS = ∠SQP and ∠RSQ = ∠QSP (by C.P.C.T)


Therefore we can say that diameter passing through Q bisects and


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