In the figure,AB is the diameter of a circle with centre O. C is any point lying on the circle such that AC=12cm and AB=13cm. Find the area of the shaded region.
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∠ ACB = 90° ( angle inscribed in semicircle is always a right angle.)
∴ Δ ABC is a right angled triangle.
AB² = AC² + BC²
13² = 12² + BC²
169 - 144 = BC²
BC² = 25
∴ BC = 5 cm
ar(ΔABC) = 1/2 × BC × AC
= 1/2 × 5 × 12
= 30 sq.cm
radius = 13/2 = 6.5 cm
ar(semicircle) = 1/2 × 3.14 × 6.5 × 6.5
= 66.33 sq.cm
ar (shaded region) = ar(semicircle) - ar(ΔABC)
= 66.33 - 30
= 36.33 sq.cm
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