Question

Draw a circle with centre $C$ and radius $3cm$. Take a point $P$ outside the circle such that $CP=6cm$. Construct tangents $PA$ and $PB$ from this point to the circle, where $A$ and $B$ are the intersection points of the tangents. Then $m\angle ACB=$ ?

• A. ${60}^{\circ }$
• B. ${120}^{\circ }$
• C. ${30}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is B ${120}^{\circ }$

Step 1: Place a compass on any point $C$ 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 $C$.

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

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

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

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 $\angle ACB$ with a protractor. $m\angle ACB={120}^{\circ }$