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If a,b,c are the sides of …

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If a,b,c are the sides of a right triangle where c is the hypotenuse ,prove that the radius of the circle which touches the sides of the triangle is given by r=a+b-c\2

    • Posted by Upendra Kumar 6 years, 11 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 11 months ago

    Sol: The circle touches the sides BC, CA, AB of the right triangle ABC at D, E and F respectively.

    Assume BC = a, CA = b and AB = c

    Then AE = AF and BD = BF, CE = CD .

    OE = OD = OF = r.

    Here OEDC is a square then CE = CD = r.i.e., b – r = AF, a – r = BF or AB = c = AF + BF = b – r + a – r

    ∴ r = (a + b - c )/2

    2Thank You

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