In the given figure, x, y and z are the sides of a right triangle, where z is the hypotenuse. Prove that the radius r…

CBSE Class 10 Maths PYQ · Circles · Triangle & Circle · 2 Marks · July 2024 · Standard

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862 Marks · July 2024 · Standard
In the given figure, $x, y$ and $z$ are the sides of a right triangle, where $z$ is the hypotenuse. Prove that the radius $r$ of the circle which touches the sides of the triangle is given by $r = \frac{x+y-z}{2}$.
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Clearly OQBP is a square
$OP = OQ = QB = BP = r$
$CS = PC = x-r$
$AS = AQ = y -r$
$AC = z = AS + CS = x - r + y-r$
Gives $r = \frac{x+y-z}{2}$
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