Question

Draw a circle of radius 5 cm. From a point 8 cm away from the centre, construct two tangents to the circle. Measure them.
(Write the steps of construction).

Answer 1

Draw $⨀(A,5cm)$ and take point $B$ in its exterior such that $AB=8cm$.
To construct:
Through $B$, tangents are to be drawn to $⨀(A,5cm)$.
Steps of construction:
1) Draw $⨀(A,5cm)$ and take point $B$ in its exterior such that $AB=8cm$.
2) Draw $\overline{AB}$.
3) Obtain the midpoint $M$ of $\overline{AB}$ by constructing its perpendicular bisector.
4) Draw $⨀(M,MA)$ intersecting $⨀(A,5cm)$ at $X$ and $Y$.
5) Draw $\overrightarrow{BX}$ and $\overrightarrow{BY}$.
Hence, $\overleftrightarrow{BX}$ and $\overleftrightarrow{BY}$ are the required tangents.
The length of tangents $\overleftrightarrow{BX}$ and $\overleftrightarrow{BY}$ is $6.2$ (approx)
i.e., $BX=BY=6.2$ cm (approx.)