Question

determine the length of a chord which is at a distance of 5cm from the centre of the circle of radius 13cm

Answer 1

Consider Length of Chord be 2x

Let O is the centre of the circle, AB is the chord and D is the point where perpendicular from the centre (OD) intersects the chord AB. Join AO which is the radius of circle.

So,

AO = 13 cm

OD = 5 cm

We know that Perpendicular Distance from the centre bisects the chord.

So AD = x

Now in right triangle ADO

AO² = AD² + OD²

13² = x² + 5²

x² = 169 - 25

x² = 144

x = 12

∴AD = 12 cm

∵ Length of Chord AB = 2AD

∴AB = 24 cm

Hence length of chord is 24 cm