Question 1018155
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A triangle with sides 17cm, 39cm and 44cm contains an inscribed circle with circumference 13 1/5 pi cm. what is the area of part of the triangle that is outside the inscribed circle? Express your answer in terms of pi. 
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The triangle with sides 17, 39 and 44 is Heronian triangle 

It has the perimeter of 100 units (halpf of the perimeter is 50 units), and the area of 330 square units. 

(To find the area, apply the Heronian formula. See the lesson <A HREF=http://www.algebra.com/algebra/homework/Surface-area/-Proof-of-the-Heron%27s-formula-for-the-area-of-a-triangle.lesson>Proof of the Heron's formula for the area of a triangle</A> in this site).

The radius of the inscribed circle is {{{330/50}}} = {{{33/5}}} = {{{6}}}{{{3/5}}} units.

(See the lesson <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-area-of-a-triangle-via-the-radius-of-the-inscribed-circle.lesson>Proof of the formula for the area of a triangle via the radius of the inscribed circle</A> in this site).

So, the circumference of the inscribed circle is {{{2*pi*r}}} = {{{13}}}{{{1/5}}} units.

Therefore, there is no need to include this data into the condition. It is calculated from the triangle side measures by the unique way.

The answer to your question is   330 - {{{pi*(33/5)^2}}}.
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