Question 5 (i) In a circle of radius 21 cm, an arc subtends an angle of 60∘ at the centre. Find: (i) the length of the arc
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Solution
Radius of the circle = 21 cm (i)ΔAOB is isosceles as two sides are equal. ∴∠A=∠B Sum of all angles of triangle = 180∘ ∠A+∠B+∠O=180∘ ⇒2∠A=180∘−60∘ ⇒∠A=120∘2 ⇒∠A=60∘ Triangle is equilateral as ∠A=∠B=∠O=60∘
Length of arc AB = 60∘360∘×2×227×21 The length of the arc is 22 cm.