A circle touches the line $L$ and the circle $C_1$ externally such that both the circles are on the same side of the line, then the locus of center of the circle is:

Let ABCD be a square of side length 2 units. $\mathrm{C}_2$ is the circle through vertices $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{C}_1$ is the circle touching all the sides of the square ABCD . L is a line through A.

A line $M$ through $A$ is drawn parallel to $B D$. Point $S$ moves such that its distances from

the line BD and the vertex A are equal. If locus of S cuts M at $\mathrm{T}_2$ and $\mathrm{T}_3$ and AC at $\mathrm{T}_1$, then area of $\Delta T_1 T_2 T_3$ is :

Circles with radii 3, 4 and 5 touch each other externally if P is the point of intersection of tangents to these circles at their points of contact. Find the distance of P from the point of contact.