Question

If the length of the common chord of two circles of radii $3$ and $4$ units, which intersect orthogonally is $\frac{k}{5},$ then the value of $k$ is

• A. $16$
• B. $7$
• C. $24$
• D. $25$

Answer 1

The correct option is C $24$


$C_1{C}_2=\sqrt{3^2+4^2}=5$
Area of $△C_{1}P{C}_2$ is,
$\frac{1}{2}\times 4\times 3=\frac{1}{2}\times C_1{C}_2\times \frac{l}{2}$
$\Rightarrow l=\frac{24}{5}$
$\therefore k=24$