Question

In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region.

Answer 1

In right triangle ABC
BC² = AB² + AC²  
= (7)² + (24)² 
= 49 + 576
= 625
∴ BC² = 625
⇒ BC = 25
Now, ∠COD + ∠BOD = 180°            (Linear pair angles)
⇒∠COD = 180° − 90° = 90°
 Now, Area of the shaded region = Area of sector having central angle (360° − 90°) −  Area of triangle  ABC

`=270^circ/360^circpi(BC)^2 - 1/2"AB" × "AC"`

`= 3/4xx3.14xxx(25/2)^2 -      1/2xx7xx24`

 =  367.97 × 84

= 283.97 cm2

Hence, the area of shaded region is 283.97 cm²