What is an inscribed circle?

In figure, $\angle ABC=69°$, $\angle ACB=31°$, find $\angle BDC$

In figure, $A, B, C$ and $D$ are four points on a circle. $AC$ and $BD$ intersect at a point $E$ such that $\angle BEC=130°$ and $\angle ECD=20°$. Find $\angle BAC$.

The circumcircle of a triangle should pass through the three vertices of the triangle.