Question

Take a point which is $9$cm away from the centre of radius $3$cm, and draw the two tangents to the circle from that point and calculate their lengths.

Answer 1

Steps of construction:

Draw a circle of radius $3$cm and draw a secant $PAB$

Draw perpendicular bisector of $PB$. Let $M$ be the midpoint of $PB$

With $M$ as centre and radius $MP$ or $MB$ draw a semi circle

Now draw a perpendicular at point $A$. Let it intersect the semicircle at point $C$.

Measure the length $PC$ and with $P$ as centre and radius $PC$ draw two arcs on the circle and mark the intersection points as $T$ and $S$.

Join the points $P,,T$ and $P,S$.