In a circle of radius 3 cm, two chords of length 2 cm and 3 cm lie on the same side of a diameter. What is the perpendicular distance between the two chords?

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Radius of circle}=3\\ & \text{Length of chord }AB=3\\ & \text{Length of chord }CD=2\\ & \Rightarrow \text{In, }\Delta OMB,\\ & OM=\sqrt{3^2-{\left(1.5\right)}^2}\\ & =\frac{3}{2}\sqrt{3}\\ & \Rightarrow \text{In, }\Delta OND,\\ & ON=\sqrt{3^2-1^2}\\ & =2\sqrt{2}\\ & \perp \text{ distance between two chords}=ON-OM\\ & =\frac{2\sqrt{2}}{1}-\frac{3\sqrt{3}}{2}\\ & =\frac{4\sqrt{2}-3\sqrt{3}}{2}\end{array}$$