Question

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)

Answer 1

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