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The diagram shows the half disc $x^2+y^2\leq 1$ for $y\geq 0$. In the region $A$, all points have $-\cos\theta\leq x\leq \sin\theta$.

For $\theta\in\left (0,\dfrac{\pi}{2}\right )$, what is the maximum value …

Point $E$ in square $ABCD$ is such that $CE=3$, $AE=4$, and $DE = 5$. Find the side length of square $ABCD$. Round your answer to four decimal places.

The diagram shows a completely connected regular nonagon. The red triangle is the smallest equilateral triangle formed by the intersection of the nonagon's diagonals. What is the ratio of the …

Given a coordinate sytem, where only integer coordinates are represented as a dot as follows:

Given two dots with $(0,0)$ and $(x,y)$ coordinates, how many dots are on the line …

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