Problem 103

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Problem 103: (2005 AMC 12B, 18)

Let $A(2,2)$ and $B(7,7)$ be points in the plane. Define $R$ as the region in the first quadrant consisting of those points $C$ such that $\triangle ABC$ is an acute triangle. What is the closest integer to the area of the region $R$? $\mathrm{(A)}\ 25 \qquad$ $ \mathrm{(B)}\ 39 \qquad$ $ \mathrm{(C)}\ 51 \qquad$ $ \mathrm{(D)}\ 60 \qquad$ $ \mathrm{(E)}\ 80 \qquad$

Solution

Exercise 103: Solution

Let $A(2,2)$ and $B(7,6)$ be points in the plane. Define $R$ as the region in the first quadrant consisting of those points $C$ such that $\triangle ABC$ is an acute triangle. What is the closest integer to the area of the region $R$?

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