Triangle with a circle

Geometry Level 3

A circle is inscribed inside an isosceles triangle with area 10 and perimeter 20 (these are measurements of the triangle, not the circle). Find the radius of the inscribed circle.


The answer is 1.

Trevor Arashiro by Trevor Arashiro , 22, USA

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1 solution

Josh Speckman
Jul 3, 2014

In any triangle, A = r s A=rs , where A A is the are, r r is the inradius, and s s is the semiperimeter (half the perimeter). The semiperimeter is 20 2 = 10 \dfrac{20}{2}=10 , and since the area is 10 10 , we have 10 r = 10 → r = 1 10r=10 \rightarrow \boxed{r=1} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Is there any other way of doing this? ANd- @trevor -what's easymoney?

Krishna Ar - 6 years, 10 months ago

is there any other method for this other than the formula ?

Mansi Bahuguna - 6 years, 9 months ago

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