Question

Prove that the line joining the midpoints of two parallel chords of a circle passes through the centre of the circle.

Answer 1

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°