Date: Wed, 18 Dec 1996 13:52:58 -0600 (CST) Subject: GeometryWho is asking: Student
Given that Triangle ABC is a right triangle and Circle O is inscribed in it find the radius of Circle O, totally in terms of a, b, and c.
If K is the center of the circle, r is its radius and P is the point where the
circle touches the side BC then BC is perpendicular to KP so the area of the
triangle KBC is (1/2)*a*r. Making the same observation for each of the other two
sides you can see that the area of the triangle ABC is (1/2)*a*r + (1/2)*b*r +
(1/2)*c*r. Since angle ABC is a right angle the area of the triangle ABC can also
be written (1/2)*a*b. Thus (1/2)*a*b = (1/2)*a*r + (1/2)*b*r +
r = a*b/(a+b+c).
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