Inscribed Triangles

Here’s a problem solving tactic we discussed at my first MathCounts team meeting yesterday.  When you see a circle inscribed in a triangle, your first instinct should be to draw radii to the points of tangency, ie, where it touches the sides of the triangle.  (It will be perpendicular to the tangent line.)  Your second instinct should be to remember that the 2 segments sharing an exterior point that are tangent to a circle are congruent.  Fill in the lengths of the radii and the tangent segments, and proceed.  (In this case, use the Pythagorean Theorem to solve for x.)

(Source: MathCounts)


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