Question

Given two circles intersecting orthogonally having length of common chord $\frac{24}{5}$ units. Radius of one of the circles is $3$ units. Radius of other circle is

• A. $6$ units
• B. $5$ units
• C. $2$ units
• D. $4$ units

Answer 1

The correct option is D $4$ units

Formula is:- Common chord$=\frac{2r_1{r}_2}{\sqrt{r_1^2+r_2^2}}$
$\frac{24}{5}=\frac{6r}{\sqrt{9+r^2}}$
$24\sqrt{9+r^2}=30r$
$\sqrt{9+r^2}=\frac{30r}{24}$
$\sqrt{9+r^2}=\frac{5r}{4}$
$9+r^2=\frac{25r^2}{16}$
$144+16r^2=25r^2$
$25r^2-16r^2=144$
$9r^2=144$
$r^2=16$
$r=4$