MathNet 2021 — Part 09 Question 79

Question 79

Inside a right circular cone with base radius $5$ and height $12$ are three congruent spheres each with radius $r$. Each sphere is tangent to the other two spheres and also tangent to the base and side of the cone. What is $r$?

$\frac{3}{2}$
$\frac{90 - 40\sqrt{3}}{11}$
$2$
$\frac{144 - 25\sqrt{3}}{44}$
$\frac{5}{2}$