Question

Draw a circle of radius $3cm$. Take a point outside the circle at a distance of $6cm$ from the centre of the circle. Construct tangents from this point to the circle. Measure the angle between the tangents and select the correct value from below.

• A. ${60}^{\circ }$
• B. ${30}^{\circ }$
• C. ${45}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

Answer: (A)

${60}^{\circ }$

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 $P-B$.

Measure $\angle APB$ with a protractor. $m\angle APB={60}^{\circ }$