Question 74
Consider the points $B$, $N$, $M$, $C$ in this order on a line, such that
$$
|BC| = 2|BM| = 4|BN|.
$$
The perpendiculars on $BC$ raised from $N$ and $M$ meet a line through $C$ at the points $A$ and $E$, respectively. Let $D$ be the intersection of $AM$ and $BE$. Prove the following statements:
a. Line $AC$ is tangent to the circumcircle of $\triangle ADB$.
b. The point $D$ is the midpoint of $AM$.
$$
|BC| = 2|BM| = 4|BN|.
$$
The perpendiculars on $BC$ raised from $N$ and $M$ meet a line through $C$ at the points $A$ and $E$, respectively. Let $D$ be the intersection of $AM$ and $BE$. Prove the following statements:
a. Line $AC$ is tangent to the circumcircle of $\triangle ADB$.
b. The point $D$ is the midpoint of $AM$.