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Properties of Triangles|Escribed Circles of a Triangle and their Radii#!#Examples

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If A,A_(1),A_(2) and A_(3) are the areas of the inscribed and escribed circles of a triangle, prove that (1)/(sqrt(A))=(1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))

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The radical center of the three circles described on the sides of a triangle as diameters is the orthocenter of a triangle.

The radii r_(1), r_(2), r_(3) of the escribed circles of the triangle ABC are in H.P. If the area of the triangle is 24 cm^(2) and its perimeter is 24 cm, then the length of its largest side is