Question

Draw a circle of radius $4cm.$ Take a point outside the circle. Without using the centre of the circle, draw two tangents to the circle from point $P.$

Answer 1

Draw a circle of radius $4cm$. Take a point $P$
outside the circle. Without using the centre of the circle,
draw two tangents to the circle from point $P$.

$Stepsofconstruction$

$STEPI$
Draw a line segment $4cm$.

$STEPII$
Take a point $P$ outside the circle and draw
a secant $PAB$ intersecting the circle at $A$ and $B$

$STEPIII$
produce $AP$ to $C$ such that $AP=CP$.

$STEPIV$
Draw a semi-circle with $CB$ as diameter.

$STEPV$
Draw $PD\perp CB$, intersecting the semi-
circle at $D$

$STEPVI$
With $P$ as centre and $PD$ as radius draw
arcs to intersect the given circle a $T$ and $T$.

$STEPVII$
Join $PT$ and $PT$. Then $PT$ and $PT$ are the required tangents.