In the Given Figure, O is the Centre of a Circle, Chord Pq ≅ Chord Rs If ∠ Por = 70° and (Arc Rs) = 80°, Find – - Geometry Mathematics 2

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Sum

In the given figure, O is the centre of a circle, chord PQ ≅ chord RS If ∠ POR = 70° and (arc RS) = 80°, find –
(1) m(arc PR)
(2) m(arc QS)
(3) m(arc QSR)  

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Solution

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(arc PQ) = m(arc RS)
⇒ m(arc PQ) = 80º               [m(arc RS) = 80º]
(1)
m(arc PR) = ∠POR = 70º           (Measure of a minor arc is the measure of its central angle)
(2)
m(arc PR) + m(arc PQ) + m(arc QS) + m(arc RS) = 360º
⇒ 70º + 80º + m(arc QS) + 80º = 360º
⇒ m(arc QS) = 360º − 230º = 130º
(3) 
m(arc QSR) = m(arc QS) + m(arc RS) = 130º + 80º = 210º

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Chapter 3: Circle - Problem Set 3 [Page 87]

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