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    Question

    The sides of a triangle are 24 cm, 26 cm and 10 cm. At

    each of its vertices, circles of radius 4.2 cm are drawn. What is the area (in cm²) of the triangle, excluding the portion covered by the sectors of the circles? (π = 22/7)
    A 27.72 Correct Answer Incorrect Answer
    B 120 Correct Answer Incorrect Answer
    C 105.86 Correct Answer Incorrect Answer
    D 92.28 Correct Answer Incorrect Answer

    Solution

    262 = 242 + 102 The given triangle is a right angle triangle with the length of the base and height 24 cm and 10 cm and the length of the hypotenuse is 26 cm Area of the triangle = (1/2) × 24 × 10 = 120 cm2 The radius of the circle in three vertices = 4.2 cm The total angle created in three circles in the vertices is 180° [∵ Sum of three angles of a triangle is 180°] The area of the triangle which is inside the common portion of the triangle and circle = (1/2) π (4.2)2 = 27.72 cm The area of the triangle excluding the circle is (120 - 27.72) = 92.28 cm2 ∴ The area excluding the portion covered by the section of the circles is 92.28 cm2.

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