Math CentralQuandaries & Queries


Question from Larissa, a student:

Find the area of the shaded region outside of a triangle inscribed (meaning the all three points of the triangle are on the circle ) in a half circle of diameter 10 inches, if one side of the triangle is the diameter and the other side is 8 inches long. (A triangle that is inscribed in a triangle is a right triangle by definition.)

Hi Larissa,

You know that the triangle is a right triangle and you know the lengths of two of the sides so you can use Pythagoras theorem to find the length of the third side. From that you can find the area of the triangle.

By the way the fact that a triangle inscribed in a semicircle is a right triangle is a theorem not a definition.


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