Question

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)

Answer 1

(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°