Find the locus of centres of circles which touch two intersecting lines.

Two tangents are drawn from an external point $\mathrm{P}$ (as shown in Fig.) such that $\angle \mathrm{OBA}=10°$. Then $\angle \mathrm{BPA}$ is

In the figure, $\mathrm{AB}$ is a diameter and $\mathrm{AC}$ is chord of a circle such that $\angle \mathrm{BAC}=30°$. If $\mathrm{DC}$ is a tangent, then $∆\mathrm{BCD}$ is