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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