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Class 10 › Mathematics › Areas Related to Circles
CBSE2026Class Class 10 · Mathematics3 Marks · Short✅ Verified
A chord PQ of a circle of diameter 28 cm subtends an angle of 90° at the centre O, where C is a point on minor arc PQ. Find the area of sector OPCQ and the area of segment PCQ.
✅ Answer & Solution
Diameter = 28 cm, so radius $r=14$ cm, $\theta=90°$.
$$\text{Area of sector }OPCQ = \frac{\theta}{360}\times\pi r^2 = \frac{90}{360}\times\frac{22}{7}\times14^2 = \frac14\times\frac{22}{7}\times196=154\ cm^2$$
$\triangle OPQ$ is right-angled at O with $OP=OQ=14$ cm:
$$\text{Area of }\triangle OPQ = \frac12\times14\times14=98\ cm^2$$
$$\text{Area of segment }PCQ = \text{Area of sector} - \text{Area of }\triangle OPQ = 154-98=56\ cm^2$$
