# In fig 3.38 ∆ QRS is an equilateral triangle. Prove that,(1) arc RS ≅ arc QS ≅ arc QR(2) m(arc QRS) = 240°.

(1) Two arcs are congruent if their measures and radii are equal.

∆ QRS is an equilateral triangle

RS = QS = QR

arc RS arc QS arc QR

(2) Let O be the centre of the circle.

m(arc QS) = QOS

QOS + QOR + SOR = 360°

3 QOS = 360° { ∆QRS is an equilateral triangle}

⇒∠ QOS = 120°

m(arc QS) = 120°

m(arc QRS ) = 360° - 120° {Measure of a major arc = 360°- measure of its corresponding minor arc}

m(arc QRS ) = 240°

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