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Question

# A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in m2? It is given that cos 53°= 35.

A

36m2

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B

44.5m2

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C

12m2

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D

72m2

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Solution

## The correct option is B 44.5m2 In △ORQ, 102 = OR2 + RQ2 102 = 62 +RQ2 ⇒ RQ2 = 64 ⇒ RQ = 8 m ∴ PQ = 2RQ = 16 m [OR is perpendicular bisector of PQ] Area of ΔOPQ = 12 × Base × Height = 12 × PQ × OR = 12 × 16 × 6 = 48 m2 Area of sector OPSQ = ∠POQ360∘ × π×r2 In ORQ, cos(∠ROQ) = adjacent sidehypotenuse = OROQ = 610 = 35 ⇒ cos( ∠ROQ) = 35 It is given that cos(53∘) = 35. Hence ∠ROQ = 53∘ ∠POQ = 2(∠ROQ) = 106∘ Area of sector POQS = POQ360 ×π×r2 = 106∘360∘ ×π×102 = 92.5 m2 Area of segment PRQS = Area of sector POQS – Area of △OPQ = 92.5 – 48 = 44.5 m2

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