Question

If $3,4$ are the radii and $5$ is the distance between the centres of two intersecting circles then the length of the common chord of the circles is :

• A. $\frac{12}{5}$
• B. $\frac{24}{25}$
• C. $\frac{24}{5}$
• D. $\frac{5}{24}$

Answer 1

Answer: (C)

$\frac{24}{5}$

L $=$length of common chord.
Distance between $C_1$ and $C_2=5$
Area of $\Delta A{C}_1{C}_2=\frac{1}{2}\times 4\times 3=6.....\left(1\right)$
and we can also write,
are of $\Delta A{C}_1{C}_2=\frac{1}{2}\times C_1{C}_2\times \frac{L}{2}$
$=\frac{5L}{4}....\left(2\right)$
From (1) & (2), $\frac{5L}{4}=6$
$\therefore L=\frac{24}{5}$