## Four Points in The Plane

We are given points $A,B,C$ and $D$ in the plane such that $AD=13$, whereas $AB=BC=AC=CD=10$. Compute the measure of $\angle{ADB}$ in degrees.
Source: NCTM Mathematics Teacher

SOLUTION

$C$ is the center of a circle of radius $10$ passing through points $A,B,D$. The central $\angle{BCA}=60^\circ$ because $\triangle{ABC}$ is equilateral. $\angle{ADB}$ is an inscribed angle that intercepts arc $AB$,
$\angle{ADB}=\displaystyle\frac{60^\circ}{2}=30^\circ$.

Answer: $30^\circ$