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In a circle having $$A(2, 2)$$ and $$B(10, 8)$$ as extremities of a diameter if a triangle $$ABC$$ is inscribed then what is the maximum possible area of the triangle?
Correct Answer: 25
The diameter is $$AB = \sqrt{8^2 + 6^2} = 10$$, so the radius is 5. With base $$AB$$ fixed, the area is greatest when $$C$$ is farthest from $$AB$$, i.e. at distance equal to the radius. The maximum area is $$\frac{1}{2} \times 10 \times 5 = 25$$ sq. units.
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