Draw $\overline{AB}$ such that $AB = 10 \, cm$. Draw $\odot(A, 3)$ and $\odot(B, 4)$. Construct tangents to each circle through the centre of the other circle.

(N/A) Data: Draw $\overline{AB}$ such that $AB = 10 \, cm$. Draw $\odot(A, 3 \, cm)$ and $\odot(B, 4 \, cm)$.
To construct: From the centre of each circle,tangents are to be drawn to the other circle.
Steps of construction:
$(1)$ Draw $\overline{AB}$ such that $AB = 10 \, cm$. Draw $\odot(A, 3 \, cm)$ and $\odot(B, 4 \, cm)$.
$(2)$ Obtain the midpoint $M$ of $\overline{AB}$ by constructing its perpendicular bisector.
$(3)$ Draw $\odot(M, MA)$ to intersect $\odot(A, 3 \, cm)$ at $S$ and $T$,and $\odot(B, 4 \, cm)$ at $X$ and $Y$.
$(4)$ Draw $\overrightarrow{AX}$ and $\overrightarrow{AY}$ as well as $\overrightarrow{BS}$ and $\overrightarrow{BT}$.
Thus,$\overleftrightarrow{AX}$ and $\overleftrightarrow{AY}$ are the tangents from $A$ to $\odot(B, 4 \, cm)$ and $\overleftrightarrow{BS}$ and $\overleftrightarrow{BT}$ are the tangents from $B$ to $\odot(A, 3 \, cm)$.