Question

a diameter PQ of a circle bisect the chord RS at the point O.if PS is parallel to RQ,prove that RS is also a diameter of the circle

Answer 1

Since PS||RQ,

∠PSO=∠QRO, and∠OPS=∠OQR

Also, ∠POS=∠QOR (vertically opposite angles).

Thus, △OQR~△OPS⇒OQOR=OPOS

⇒OQOR=OPOR [∵OR=OS as it is given that O bisects RS]⇒OQ=OP

⇒O is the midpoint of PQ.

⇒O is the centre of the circle.

Now, since RS passes through O, it means that RS passes through the centre of the circle.

⇒RS is a diameter of the circle.

Hence Proved

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Answer 2

Answer:

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