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Question
In a circle of diameter 40 cm, a chord is of length 20 cm. Find the length of the minor arc of the chord
Solution
O = centre of the circle
PQ = diameter = 40 cm
∴ OQ = 20 cm
Radius = 20 cm
⇒ OA = OB = 20 cm
Chord AB = 20 cm
OC ⊥ r AB
∴ AC = CB = 10 cm
Now from the right angled triangle OCB
sin θ = `10/20 = 1/2`
⇒ θ = `pi/6`
So ∠AOB = `2 xx pi/6 = pi/3` = 60
Now r = 20 cm, θ = `pi/3`
So arc AB = `60/360 2pi"r"`
= `60/360 xx 2 xx pi xx 20`
= `(20pi)/3` cm
or
= 20.95 cm
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