Q18 of 141 Page 400

In the adjoining figure, is a diameter of a circle with center If and are two chord such that prove that


Draw, OPAB and OQCD


In triangle OBP and triangle OQC,


∠OPB = ∠OQC [Angle = 90°]


∠OBP = ∠OCD [Alternate angle]


OB = OC [Radius]


By side-angle-side criterion of congruence


ΔOBP ≅ ΔOQC


∴ OP = OQ


The chords equidistant from the center are equal.


∴ AB = CD Proved.


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