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a,b and c are the sides of the triangle of which, c is the hypotenuse. A circle of radius r is inscribed in it touching all sides then prove that r=a+b-c/2

Posted by Khushi Agrawal 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

The circle touches the sides BC, CA, AB of the right triangle ABC at D, E and F respectively. Let BC = a, CA = b and AB = c
Now, AF = AE and BD = BF
⇒ AF = AE = AC - CE and BF = BD = BC - CD
⇒ AF = b - r and BF = a - r ( {tex}\because{/tex} OEDC is a square)
⇒ AF + BF = ( b - r ) + (a - r)
⇒ AB = a + b - 2r
⇒ c = a + b - 2 r
⇒ r = {tex}\frac { a + b - c } { 2 }{/tex}

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CBSE > Class 10 > Mathematics