Question

Draw a circle of radius $3cm$. From a point$P,7cm$ away from it centre draw two tangents to the circle. Measure the length of each tangent.

Answer 1

(i) Draw a circle with centre $O$ and radius $3cm$.

(ii) Let $OP=7cm$

(iii) Join $OP$. Draw its perpendicular bisector which intersects $PO$ at $M$.

(iv) With $M$ as centre, draw a circle of radius $MO$ such that it passes through point $O$ and $P$.

(v) Let this circle intersect the original circle at points $R$ and $Q$.

(vi) $PQ$ and $PR$ are the required tangents.

Measure of tangents: Join $OQ$

Consider right $\Delta PQO$ [As $OQ\perp PQ$]

By Pythagoras Theorem,

$\Rightarrow P{O}^2=O{Q}^2+P{Q}^2$

$\Rightarrow 7^2=3^2+P{Q}^2$

$\Rightarrow 49-9=P{Q}^2$

$\therefore PQ=2\sqrt{10}cm$