Theory question 109
Mensuration of Plane ShapesThe diameter of a circle centre O is 26 cm. If a chord PQ is drawn such that it is 5 cm from O to the centre of the chord, calculate, correct to the nearest whole number, the: (a) ∠POQ; (b) area of the minor segment formed by the chord PQ. [Take π = 22/7]
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Model answer
(a) Radius = 13 cm; cos(½∠POQ) = 5/13 ⇒ ½∠POQ ≈ 67.38° ⇒ ∠POQ ≈ 135°
(b) Area of sector = 135/360 × 22/7 × 13² ≈ 199.2 cm²
Area of triangle POQ = ½ × 13² × sin 135° ≈ 59.8 cm² (half-chord = 12 cm gives exactly 60 cm²)
Area of minor segment ≈ 139 cm²
Explanation
The line from the centre to the middle of a chord is perpendicular to it.