Question

In the following figure O is the centre of the circle chord PQ and RS intersect inside the circle at M . Prove that: Angle POR + Angle QOS = 2Angle PMR.​

Answer 1

Answer:

O is the centre of the circle.

chord PQ≅ chord RS (Given)

⇒ arc PQ≅ arc RS (Correspondidng arcs of congruent chords of a circle are congruent)

⇒m(arcPQ)=m(arcRS)

⇒m(arcPQ)=80

o

[m(arcRS)=80

o

]

(1) m(arcPR)=∠POR=70

o

(Measure of a minor arc is the measure of its central angle)

(2) m(arcPR)+m(arcPQ)+m(arcQS)+m(arcRS)=360

o

⇒70

o

+80

o

+m(arcQS)+80

o

=360

0

⇒m(arcQS)=360

o

−230

o

=130

o

(3) m(arcQSR)=m(arcQS)+m(arcRS)=130

o

+80

o

=210

o