In the figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R,S and P,Q respectively. Prove that `:` seg SQ `||` seg RP.

In the figure, two circles intersect at points M and N. Secants drawn

1.	In the figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R,S and P,Q respectively. Prove that `:` seg SQ `\|\|` seg RP.
Answer» Draw seg MN `square ` MRPN is cyclic and `/_ MNQ ` is its exterior angle. `/_ MNQ = /_ MRP ` ….(1) …...(Corollary of cyclic quadrilateral theorem ) `square ` MNQS is cyclic `:. /_ MNQ + /_ MSQ = 180^(@0` …(Theorem of cyclic quadrilateral ) `:. /_ MRP + /_MSQ = 180^(@)` ....[From (1) ] `:. /_SRP + /_ RSQ = 180^(@)` .....(R-M-S) `:.` seg `SQ \|\| ` seg `RP ` ....(interior angles test for parallel lines )

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In the figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R,S and P,Q respectively. Prove that `:` seg SQ `||` seg RP.

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