Q. 24.0( 38 Votes )

# In fig 3.38 ∆ QRS is an equilateral triangle. Prove that,

(1) arc RS ≅ arc QS ≅ arc QR

(2) m(arc QRS) = 240°.

Answer :

(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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