Question

In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110° at the centre of the circle. Find the area of the circle.

Answer 1

Given: r = 6 cm, chord AB = 10 cm, ∠AOB = 110°.

Step-wise calculation:

1. Area formula:

A = πr²

2. Substitute r = 6 cm:

A = π × 6²

= 36π cm²

3. Decimal value: 

36π ≈ 36 × 3.1416

= 113.10 cm²

4. The chord given is slightly inconsistent with r = 6 and angle 110°, since chord = `2r sin(θ/2) = 12·sin55°` ≈ 9.83 cm ≠ 10 cm. 

If one used the chord and angle to find r, `r ≈ 5/sin55° ≈ 6.103` cm and area ≈ 117.05 cm².

Area of the circle = 36π cm² ≈ 113.10 cm².