Radius of a Circle Inscribed in a TriangleDate: 06/02/99 at 19:51:38 From: Michael Subject: Radius of an inscribed circle There is a drawing of a right triangle with sides of lengths 3, 4, and 5. A circle is inscribed in the triangle so that each side is tangent to the circle. The question is: What is the radius of an inscribed circle of a triangle with sides 3, 4, and 5? I have tried a few different methods, none of which seems to work. What should I do? Date: 06/03/99 at 08:03:23 From: Doctor Floor Subject: Re: Radius of an inscribed circle Hi, Michael, Thanks for your question! Let's consider the general situation of a right triangle: B | \ | Z I is the center of the inscribed circle. X I \ X,Y and Z are the points where the inscribed | \ circle meets the sides, so XI = YI = ZI = r. C---Y----------A I write a = BC (length), b = AC and c = AB. We know that area(ABC) = 0.5*a*b .........................[1]. Also area(ABC) = area(ABI) + area(CIA) + area(BCI) = 0.5*r*a + 0.5*r*b + 0.5*r*c = 0.5*r*(a+b+c) .........................[2]. From [1] = [2] we find the formula: r = a*b/(a+b+c). I suppose you can do the rest yourself now. I hope this helps you out. Best regards, - Doctor Floor, The Math Forum http://mathforum.org/dr.math/ |
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