Question 154
Two circles $C_1, C_2$ with different radii are given in the plane. They touch each other externally at $T$. Consider any points $A \in C_1$ and $B \in C_2$, both different from $T$, such that $\angle ATB = 90^\circ$.
a. Show that all such lines $AB$ are concurrent.
b. Find the locus of midpoints of all such segments $AB$.
a. Show that all such lines $AB$ are concurrent.
b. Find the locus of midpoints of all such segments $AB$.