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    Subject

    Quantitative Aptitude

    Topic

    Mensuration

    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)?

    ক)
    28.5
    খ)
    31.5
    গ)
    33.33
    ঘ)
    36
    ঙ)
    42.5

    Explanation

    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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