Question

diagonals of a quadrilateral pqrs intersect in point m if 2pm =mr ,2mq=sm then prove that ts=2pq plz give right answer fast​

Answer 1

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Asked on December 26, 2019 by

Shreyansh Bhosale

The diagonals PR and QS of a cyclic quadrilateral PQRS intersect at X. The tangent at P is parallel to QS. Prove that PQ=PS.

If m∠PQS=50

o

, then m(∠PRS) is

426918

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ANSWER

Chords PS subtends.

∠PQS and ∠PRS in the same segment.

∠PQS=∠PRS

∠PQS=80° [L subtended by same chord / arc in same segment in equal]

∠PQR=80+50=130

∠PQR+∠PSR=180(sum of opposite angle of cyclic quadrilaterals is 180°)

130+∠PSR=180

∠PSR=50°

And as we know ∠PQS=50

∴∠PRS=360−(∠PQS+∠PSR)

=360−100

=260