Art of Problem Solving

2025 AMC 10A Problems/Problem 25: Difference between revisions

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<imath>\textbf{(A) }25 \qquad \textbf{(B) }26 \qquad \textbf{(C) }27 \qquad \textbf{(D) }28 \qquad \textbf{(E)}  29 \qquad</imath>
<imath>\textbf{(A) }25 \qquad \textbf{(B) }26 \qquad \textbf{(C) }27 \qquad \textbf{(D) }28 \qquad \textbf{(E)}  29 \qquad</imath>


==Solution 1 (in progress)==
==Solution 1 (Calculus (the actual way I used))==
Note: this solution is only recommended for those who have integrated <imath>cos^2(x)</imath> too many times.

Revision as of 14:06, 6 November 2025

2025 AMC 10A Problems/Problem 25

A point $P$ is chosen at random inside square $ABCD$. The probability that $\overline{AP}$ is neither the shortest nor the longest side of $\triangle APB$ can be written as $\frac{a + b \pi - c \sqrt{d}}{e}$, where $a, b, c, d,$ and $e$ are positive integers, $\text{gcd}(a, b, c, e) = 1$, and $d$ is not divisible by the square of a prime. What is $a+b+c+d+e$?

$\textbf{(A) }25 \qquad \textbf{(B) }26 \qquad \textbf{(C) }27 \qquad \textbf{(D) }28 \qquad \textbf{(E)}  29 \qquad$

Solution 1 (Calculus (the actual way I used))

Note: this solution is only recommended for those who have integrated $cos^2(x)$ too many times.