Question

The two circles intersect at $P$ and $Q$ as shown in figure. If $PQ$ is equal to the radius of the circle with centre $C_2$, and it is equal to $8 cm$ and radius of the circle with centre $C_1$ is $5 cm$, then calculate the distance between the centres (in $cm$ ).

• A. $\sqrt{3}+4 \sqrt{3}$
• B. $7 \sqrt{3}+3$
• C. $3 \sqrt{10}$
• D. $\sqrt{7}+\sqrt{3}$

Answer 1

Answer: (A)

Let $A B$ and $C_1 C_2$ intersect at $O$.
$OC _1=\sqrt{5^2-4^2}=\sqrt{25-16}=\sqrt{9} $
$OC _2=\sqrt{8^2-4^2}=\sqrt{64-16}=\sqrt{48}$
$\therefore OC _1+ OC _2=\sqrt{3}+4 \sqrt{3}$