Question

A chord of a circle of radius 14 cm make a right angle at the centre. Find the area of the minor and major segments of the circle.​

Answer 1

Given radius (r) =14cm

⇒  Area of sector OABO = $\frac{0}{360}$​πr²

∴  Area of sector OABO = $\frac{90}{360}$ × $\frac{22}{7}$ × $(14^{2} )$

                                        = 154cm²

⇒  Area of right angled △OAB = $\frac{1}{2}$ × 14 × 14

                                                   = 98cm²

∴  Area of the minor segment of the circle = Area of sector OABO - Area of right angled △ABO

∴  Area of the minor segment of the circle = (154 − 98) cm²

                                                                       = 56cm²

⇒  Area of circle = πr² = $\frac{22}{7}$ × 14 × 14

                                     = 616cm²

⇒  Area of the major segment of the circle = Area of circle - Area of minor segment.

∴  Area of the major segment of the circle = (616 − 56)cm²

                                                                      = 560cm²

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