Question

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

• A. Different
• B. Can't say
• C. Equal
• D. May be equal or not but doesn't depend on the distance from the centre.

Answer 1

The correct option is C

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 $\Delta$ AOB
$AB=2\sqrt{r^2-x^2}$
Using Pythagoras theorem in $\Delta$ COD
$CD=2\sqrt{r^2-x^2}$
So the lengths of the two chords are alwaus always equal if their perpendicular distance from the centre to the chords is equal