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The measure of an inscrbed angle is 1/2 of the measure of the intercepted arc. This is a theorem. An inscribed angle is an angle with its vertex on the circle and the sides of it contain chords of the circle.
The maximum inscribed angle that can be formed in this instance is 90 degrees since the maximum angle of the arc that can be formed is 180 degrees (A semi-circle). By this theorem the inscribed angle becomes 90 degrees which forms the height of the triangle. Now apply the formula 1/2 * b * h which gives us 1/2.