Question

Draw a circle of radius $6cm$. Take an external point $P$ at a distance of $10cm$ from centre and construct tangents to the circle from $P$. The sum of the lengths of the tangent segments (in $cm$) is:

Answer 1

Step 1: Draw a circle by keeping the compass on point $O$ and taking radius $=6cm$

Step 2: Take a point $P$ outside the circle at a distance of $10cm$ from centre $O$ with the help of a ruler. Draw segment $OP$.

Step 3: Place the compass on point $P$ and draw two arcs above and below line $OP$.

Step 4: Repeat the above step by placing the compass on point $O$ such that the two arcs from $O$ intersect the two arcs from $P$.

Step 5: Join the intersection points of the arcs to obtain the perpendicular bisector of $OP$. Let this perpendicular bisector intersect $OP$ at point $M$.

Step 6: Place the compass on point $M$ and draw a circle with radius $=PM=OM$. Let this circle intersect the circle with centre $O$ at points $Q$ and $R$.

Step 7: Join $P-Q$ and $P-R$.

$PQ$ and $PR$ are the required tangents to the circle with radius $=6cm$ from an external point $P$ at a distance of $10cm$.

By measuring $PQ$ and $PR$, we get $PQ=PR=8cm$

$\therefore$ sum of the lengths of the tangents $=8+8=16cm$