Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre. -Maths 9th

Prove that the line joining the mid-points of two parallel chords of a circle passes through the centre. -Maths 9th
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Let AB and CD be two parallel chords having P and Q as their mid-points, respectively. Let O be the centre of the circle. Join OP and OQ and draw OX | |  AB | | CD. Since, Pis the mid-point of AB.  ⇒ OP ⊥ AB ⇒ ∠APO = ∠BPO = 90° But OX | | AB  ∴ ∠POX = ∠APO [alternate interior angle] ⇒  ∠POX =  90°    Similarly, ∠XOQ =  90° Now,  ∠POX + ∠XOQ  = 90° + 90°  = 180°   so, POQ is a straight line . Hence proved     
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Last Answer : hope its clear

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