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?

Solution (By Examveda Team)

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