Question

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

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

Answer 1

The correct option is D 4 units

Formula used : Common chord = $\frac{2r_1{r}_2}{\sqrt{r_1^2+r_2^2}}$$\frac{24}{5}=\frac{2\left(3\right)r}{\sqrt{3^2+r^2}}⟹\frac{24}{5}=\frac{6r}{\sqrt{9+r^2}}⟹24\sqrt{9+r^2}=30r⟹\sqrt{9+r^2}=\frac{30r}{24}=\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$