Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90°, as shown in the given figure.

Given:

Radius of Circle = 35 cm

∠AOB = 90°

∵ Area of Sector = × πr^{2}

= × × 35 × 35

= cm^{2}

∵ ∆ AOB is right-angled triangle.

∴ Area of ∆ AOB = × OA × OB

= × 35 × 35

= cm^{2}

Now, Area of Minor Segment ACB

= Area of Sector – Area of ∆AOB

= - = = 350 cm^{2}

Area of Circle = πr^{2}

= × 35 × 35

= 22 × 5 × 35

= 3850 cm^{2}

Thus, Area of Major Segment = Area of Circle – Area of Minor Segment = 3850 – 350 = 3500 cm^{2}

__Hence, the area of the major segment is 3500 cm ^{2}.__

51