Areas Related to Circles · Class 10 · CBSE Mathematics

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment. (Use pi = 3.14)

Practice question from Areas Related to Circles (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

hard · Subjective · Q-49EA92

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding minor segment. (Use $\pi = 3.14$ )

Answer: The area of the minor segment is equal to the area of the minor sector minus the area of the right-angled triangle formed by the radii and the chord. Area of sector =

\frac{90^\circ}{360^\circ} \times 3.14 \times 10^2 = \frac{1}{4} \times 314 = 78.5\text{ cm}^2

. Area of triangle =

\frac{1}{2} \times 10 \times 10 = 50\text{ cm}^2

. Therefore, area of minor segment =

78.5 - 50 = 28.5\text{ cm}^2

Solution

Subtract the area of the right triangle ( $50\text{ cm}^2$ ) from the area of the 90-degree sector ( $78.5\text{ cm}^2$ ) to get $28.5\text{ cm}^2$ .

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