A triangle and an incircle

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Question from Max, a student:

On my Geometry Test about tangent, chord, and secant lengths, my teacher gave an extremely difficult problem.
It was a Circle inscribed in a Triangle with all triangle sides being tangents and lengths were given. My class was told to find the length of each segment of the line.
The points on each line were the vertexes of the triangle, and the point where the line hits the circle.
Please explain how someone could do this.

Max,

Use the theorem that THE TWO TANGENTS FROM A POINT TO A CIRCLE HAVE THE SAME LENGTH. For a triangle ABC let x be the length of the tangents from A to the incircle, y from B, and z from C. Then compute a + b - c in terms of x, y, and z. If you need more help, look up the term "incircle" on the internet.

Chris

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