Question

PQ and RS are two parallel chords of a circle and lines RP and SQ intersect at point M . Prove that MP=MQ​

Answer 1

Answer:

In cyclic quadrilateral PQRS:

∵PQ∣∣RS

⇒PR=QS

We know from the properties of circle, OP⋅OR=OQ⋅OS

Above can also be written as OP⋅(OP+PR)=OQ⋅(OQ+QS)

⇒OP

2

−OQ

2

=QS(OQ−OP)

⇒(OP−OQ)(OP+OQ+QS)=0

∴OP=OQ

Step-by-step explanation:

hope u understood:)