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Question

If the perpendicular distances of two chords are equal from the centre of a circle then the length of the two chords is
  1. Equal

  2. May be equal or not but doesn't depend on the distance from the centre.

  3. Different

  4. Can't say


Solution

The correct option is A

Equal



Let the centre of the circle be O, be the radius and x be the perpendicular distance of the chords from the centre of the circle.
Using Pythagoras theorem in Δ AOB
AB=2r2x2
Using Pythagoras theorem in Δ COD
CD=2r2x2
So the lengths of the two chords are alwaus always equal if their perpendicular distance from the centre to the chords is equal

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