RO-TST 1988 Problem 7

In the plane there are given the lines $\ell_1$ , $\ell_2$ , the circle $\mathcal{C}$ with its center on the line $\ell_1$ and a second circle $\mathcal{C}_1$ which is tangent to $\ell_1$ , $\ell_2$ and $\mathcal{C}$ . Find the locus of the tangent point between $\mathcal{C}$ and $\mathcal{C}_1$ while the center of $\mathcal{C}$ is variable on $\ell_1$ .

Mircea Becheanu