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