Question

The line $AB$ divides the line segment $OP$ in the ratio _____

• A. $1:1$
• B. $3:4$
• C. $1:2$
• D. $9:16$

Answer 1

Answer: (D)

$9:16$

Step 1: Place a compass on any point $O$ on the paper and draw a circle of radius $6cm$.

Step 2: Mark a point $P$ outside the circle at a distance of $10cm$ from $O$.

Step 3: Place the compass on $P$, take radius of more than $5cm$ and draw two arcs on both sides of line $OP$. With the same radius, mark two arcs from point $O$ which intersect the arcs drawn from $P$.

Step 4: Join the intersection points of the arcs to obtain the perpendicular bisector of $OP$. Mark the mid point of $OP$ as $M$.

Step 5: Place the compass on $M$ and draw a circle with radius $=PM=OM$

Step 6: Mark the intersection points of the circle obtained in step $5$ and the original circle as $A$ and $B$. Join $P-A$ and $P-B$.

Draw segment $AB$ and let it intersect line $OP$ at $R$. Measure $PR$ and $OR$ with the help of a ruler. We get $PR=6.4cm$ and $OR=3.6cm$. Therefore, $R$ divides $OP$ in the ratio $OR:PR=3.6:6.4=9:16$