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Textbook Page No. 72, , Question 1., , Prove that chords of the same length, in a circle are at the same distance, from the centre., , Answer:, , , , AB, CD are the chords of same length., AB = CD, , AP = %AB (Perpendicular from the, centre of a circle to a chord bisects, the chord), , Similarly CQ = %CD, , AP = CQ [Since AB = CD], , Consider the right angled triangle, AAOP and ACOQ, , OP? = OA? - AP?, , OP? = OB? - CQ? [Since OA = OB, AP =, , rey

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OP? = OQ?, , “OP =0Q, , So, the chords of the same length in a, circle are at the same distance from, the centre., , Question 2., , Two chords intersect at a point ona, circle and the diameter through this, point bisects the angle between the, chords. Prove that the chords have, the same length., , Answer:, , OA = OC (radius of the same circle), , OB = OB (common side), A, , ZOBA = ZOBC (given), , ZBAO = 2BCO [Base angle of, isosceless triangle AOCB & AOCA]

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ZAOB = ZBOC;, , “. AAOB = ABOC, , So the sides AB and BC opposite to, equal angles are also equal., , Question 3., , In the picture on the right, the angles, between the radii and the chords are, equal. Prove that the chords are of, the same length.