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प्रश्न
In figure, O is the centre of a circle, chord PQ ≅ chord RS. If ∠POR = 70° and (arc RS) = 80°, find
(i) m(arc PR)
(ii) m(arc QS)
(iii) m(arc QSR)
उत्तर
(i) m(arc PR) = m∠POR ...[Definition of measure of arc]
∴ m(arc PR) = 70°
(ii)
chord PQ ≅ chord RS .....[Given]
∴ m(arc PQ) = m(arc RS) = 80° .....[Corresponding arcs of congruent chords of a circle are congruent]
Now,
m(arc QS) + m(arc PQ) + m(arc PR) + m(arc RS) = 360° ...[Measure of a circle is 360°]
∴ m(arc QS) + 80° + 70° + 80° = 360°
∴ m(arc QS) + 230° = 360°
∴ m(arc QS) = 130°
(iii) m(arc QSR) = m(arc QS) + m(arc SR) = 130° + 80° ...[Arc addition property]
m(arc QSR) = 210°
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