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A chord of a circle ofradius 15 cm subtends anangle of 60° at the center areaof the corresponding minorsegment of the circle is20'4478 cm2 |
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Answer» please follow me Step-by-step explanation: ANSWER In the mentioned figure, O is the centre of CIRCLE, AB is a chord AXB is a major arc, OA=OB= radius = 15 cm Arc AXB subtends an angle 60 o at O. Area of sector AOB= 360 60
×π×r
= 360 60
×3.14×(15) 2
=117.75cm 2
Area of MINOR segment (Area of Shaded region) = Area of sector AOB− Area of △ AOB By trigonometry, AC=15sin30 OC=15cos30 And, AB=2AC ∴ AB=2×15sin30=15 cm ∴ OC=15cos30=15 2 3
=15× 2 1.73
=12.975 cm ∴ Area of △AOB=0.5×15×12.975=97.3125cm 2
∴ Area of minor segment (Area of Shaded region) =117.75−97.3125=20.4375 cm 2
Area of major segment = Area of circle − Area of minor segment =(3.14×15×15)−20.4375 =686.0625cm 2
solution |
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