Question

Draw a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents.

Answer 1

Draw a circle of radius $6cm$ with center $O$. Draw a line segment of $10cm$ away from point/center $O$

Mark midpoint of $OP$ and draw a circle of radius $OQ=5cm$

This circle cuts the initial circle at two points $M$ and $N$. Join $MP$ and $NP$ are the required tangents.

We know, $PM=PN$ (tangent to a circle from external point)

In $△ONP,$

$(ON{)}^2+(PN{)}^2=\left(OP{)}^2\right(PN{)}^2=(OP{)}^2-(ON{)}^2=(10{)}^2-6^2=64PN=8cm$