MathNet 2019-part-02 — 184 problems (EN–VI) Question 64

Let $ABCD$ be a trapezoid with $AD \parallel BC$, such that the side $CD$ is tangent to the circle with diameter $AB$. If $G$ is the midpoint of $CD$ and $CD = 8\ \mathrm{cm}$, determine the length of the height $GF$.