A circle is drawn with diameter 20 cm. A point P is taken on the circle such that the triangle PQR formed by P with diameter QR is isosceles. What will be the area of minor segment formed by chord PQ (in square cm)?
Solution
Correct Answer: Option A
Let centre of circle be M.
Radius of circle = (1/2) × 20 cm = 10 cm
If PQR is isosceles, and QR is diameter, angle P will be right, as angle in a semicircle is right.
⇒ QP and RP will be equal sides of triangle PQR and hence will subtend equal angles at centre.
Together they subtend an angle of 180°.
⇒ PQ will subtend an angle of 90°.
∴ Area of minor segment = Area of sector – Area of triangle PMQ = ¼ π × 10 × 10 – ½ × 10 × 10 = 28.5 square cm
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