Question

In the adjoining figure, A is the centre of the circle. ∠ABC = 45° and AC = 7√2 cm. Find the area of segment BXC, (π = 3.14)

Answer 1

In ∆ABC, 

AC = AB … [Radii of same circle] 

∴ ∠ABC = ∠ACB …[Isosceles triangle theorem] 

∴ ∠ABC = ∠ACB = 45° 

In ∆ABC,

∠ABC + ∠ACB + ∠BAC = 180° … [Sum of the measures of angles of a triangle is 180° ] 

∴ 45° + 45° + ∠BAC = 180° 

∴ 90° + ∠BAC = 180° 

∴ ∠BAC = 90° 

Let ∠BAC = θ = 90°

∴ The area of segment BXC is 27.93 cm² .