Printable

2015 AMC 10A Problem 25

Include the solution Back to the problem

2015 AMC 10A Problem 25AMC 10 Step by Step

Name: Date: September 13, 2026

Geometric Probability · difficulty 4 of 5 · about 8 min · position P21-25

Let $S$ be a square of side length $1$ . Two points are chosen at random on the sides of $S$ . The probability that the straight-line distance between the points is at least $\tfrac12$ is $\tfrac{a-b\pi}c$ , where $a$ , $b$ , and $c$ are positive integers with $\gcd(a,b,c)=1$ . What is $a+b+c$ ?

A)
$59$
B)
$60$
C)
$61$
D)
$62$
E)
$63$

2015 AMC 10A Problem 25

Working