SOLUTION: A triangle has two 13-cm sides and a 10-cm side. The largest circle that fits inside this triangle meets each side at a point of tangency. These points of tangency divide the sides

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Question 1158199: A triangle has two 13-cm sides and a 10-cm side. The largest circle that fits inside this triangle meets each side at a point of tangency. These points of tangency divide the sides of the triangle into segments of what lengths? What is the radius of the circle?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

radius-circle-inscribed-isosceles-triangle.png


If the base length of the isosceles triangle is b+and the two legs are a then prove that the radius of the inscribed circle is given by formula:

r=%28b%2F2%29sqrt%28%282a-b%29%2F%282a%2Bb%29%29

if a=13 and b=10, we have

r=%2810%2F2%29sqrt%28%282%2A13-10%29%2F%282%2A13%2B10%29%29

r=5sqrt%2816%2F36%29

r=5%28sqrt%2816%29%2Fsqrt%2836%29%29

r=5%284%2F6%29

r=20%2F6

r=3.33in