Let $AB$ be a diameter of semicircle $h$. On this semicircle there is point $C$, distinct from points $A$ and $B$. Foot of perpendicular from point $C$ to side $AB$ is point $D$. Circle $k$ is outside the triangle $ADC$ and at the same time touches semicircle $h$ and sides $AB$ and $CD$. Touching point of $k$ with side $AB$ is point $E$, with semicircle $h$ is point $T$ and with side $CD$ is point $S$ $a)$ Prove that points $A$, $S$ and $T$ are collinear $b)$ Prove that $AC=AE$
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2016
Tags: geometry, collinear, semicircle, touching circles