Question 1190317
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A circle is inscribed in a right triangle that has a hypotenuse of 182 cm. 
If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle?
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<pre>
For any right triangle, the radius of the inscribed circle is 

    r = {{{(a + b - c)/2}}},     (1)


where "a" and "b" are the legs lengths and "c" is the hypotenuse length.


We are given the perimeter P = a + b + c = 420 cm  and  the hypotenuse length  c= 182 cm,


therefore, we can easily compute the radius of the inscribed circle

    r = {{{((a + b + c) - 2c)/2}}} = {{{P/2-c}}} = {{{420/2-182}}} = 210 - 182 = 28 centimeters.    <U>ANSWER</U>
</pre>

Solved.


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Regarding formula &nbsp;(1) &nbsp;and its proof, &nbsp;see the lesson


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/The-radius-of-a-circle-inscribed-into-a-right-angled-triangle.lesson>The radius of a circle inscribed into a right angled triangle</A>


in this site.