Construction of Polygon In and Around a Circle

What is a circumscribed polygon?

What is an inscribed circle?

The construction of incircle is being done by obtaining the point of intersection of two perpendicular of sides and bisector of two angles. 

Can we construct a Hexagon of a side  $4 \mathrm{cm}$.

We can construct a regular hexagon of side $2.6 \mathrm{cm}$.

$ABCD$ is a cyclic quadrilateral, whose diagonals intersect at a point $E$. If $\angle DBC=70°$, $\angle BAC=30°$, find $\angle BCD$

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 $\angle BAC$.

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