C. Given below is a circle with centre O Chord PQ - Chord RS
Prove that m 2POQ = m AROS
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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
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