Question

Draw $\overline{PQ}$, where $PQ=10cm$. Draw circle $\odot (P,4)$ and $\odot (Q,3)$. Draw tangents to each circle from the centre of the other circle. Write points of construction.

Answer 1

Data: Draw $\overline{PQ}$ such that $PQ=10cm$. Draw circle $\odot (P,4)$ and $\odot (Q,3)$
To Construct: From the centre of each circle, tangents are to be drawn to the circle.
Steps of Construction:
(i) Draw $\overline{PQ}$ such that $PQ=10cm$. Draw circle $\odot (P,4)$ and $\odot (Q,3)$.
(ii) Obtain the midpoint $M$ of $\overline{PQ}$ by constructing its perpendicular bisector.
(iii) Draw $\odot (M,MP)$ to intersect $\odot (Q,3)$ at $S$ and$T$ and $\odot (P,4)$ at $X$ and $Y$.
(iv) Draw $\overline{QX}$ and $\overline{QY}$ as well as $\overline{PS}$ and $\overline{PT}$.
(v) Thus $\overline{QX}$ and $\overline{QY}$ are the tangents from $Q$ to $\odot (P,4)$ and $\overline{PS}$ and $\overline{PT}$ are the tangents from $P$ to $\odot (Q,3)$