Random Point in Circle - Problem Statement

Generate a random point uniformly in a circle of radius $r$. This isn't DP, but illustrates probability concepts.

Wrong approach: random angle + random radius. Points cluster near center because area grows with $r^2$. Correct: random angle, radius = $r \cdot \sqrt{\text{random}}$. The square root compensates for area growth. Alternatively: rejection sampling. Pick random $(x, y)$ in square, accept if $x^2 + y^2 \leq r^2$.