Question

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.

Answer 1

Answer:

∠ 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