Question

In 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)

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°