Question

$r_{1}, r_{2}>0$ and if $C_{1}, C_{2}$ are centres of the two circles having only two common tangents and $C_{1} C_{2}=r_{1}+r_{2}$, then which of the following is correct

• A. $r_{1}, r_{2}$ are the radii of the two circles
• B. The common chord may divide the line joining the centres in the ratio $r_{1}: r_{2}$
• C. $r_{1}, r_{2}$ are always the distances of the centres from the common tangent of the two circles
• D. external centre of similitude divides $C_{1} C_{2}$ in the ratio $r_{1}: r_{2}$

Answer 1

Answer: (B)

When two circles, having centre have only two common tangents and $c_{1} c_{2}=r_{1}+r_{2}$, then the common chord divide the line joining the centres in the ratio $r_{1}: r_{2}$.