Question

In Given figure, two circles intersect at point $M$ and $N$. Secants drawn through $M$ and $N$ intersect the circles at points $R$, $S$ and $P,Q$ respectively. Prove that : $segSQ\parallel segRP$

Answer 1

The segments are said to be parallel only if the chords through their end of end points are parallel

For a circle the chords at corresponding points are parallel

So for first circle

$RP||MN\cdots \left(1\right)$

So for Second circle

$SQ||MN\cdots \left(2\right)$

From $\left(1\right),\left(2\right)$

$⟹RP||SQ$

Hence the segments are parallel.