Question

Draw a circle of radius $4cm.$ Take a point $P$ on it. Without using the centre of the circle, draw a tangent to the circle at point $P.$

Answer 1

We follow the steps of constructions:

Steps of construction
$STEPI$
Draw any chord $PQ$ through the given point $P$ on the circle.

$STEPII$
Take a point $R$ on the circle and join $P$ and $Q$ to a point $R$.

$STEPIII$
Construct $\angle QPY=\angle PRQ$ and on the opposite side of the chord

$PQ$.

$STEPIV$
Produce $YP$ to $X$ to get $YPX$ as the required tangent.