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Area of a Triangle inside the Incircle

Let ABC be a triangle, the radius of its incircle, and the radius of its circumcircle. Let D and E be the feet of the perpendiculars drawn from the center I of the incircle onto AB and AC, respectively. Then the area of the triangle IDE is .

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The statement of the theorem is in Problem 81. Triangle Area, Side, Inradius, Circumradius.

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"Area of a Triangle inside the Incircle" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/AreaOfATriangleInsideTheIncircle/
Contributed by: Jay Warendorff
After work by: Antonio Gutierrez
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