Question

a chord of length 24 cm is at a distance of 5 cm from the centre of the circle find the length of the chord of the same circle which is at a distance of 12 cm from the centre prove

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Answer 1

Let us consider AB as the chord of length 24 cm and O as the centre of the circle.

And the we will take OC as the perpendicular drawn from the centre O to AB.

Here, the perpendicular to a chord, from the centre of a circle, bisects the chord.

So, AC = CB = 12 cm

In △ OCA,

OA² = OC² + AC² [Using Pythagoras Theorem]

Substituting the values

OA² = 52 + 122

OA = 169

So we get

OA = 13 cm

Therefore, radius of the circle is 13 cm.

Consider A’B’ as the new chord at a distance of 12 cm from the centre.

(OA’)² = (OC’)² + (A’C’)²

Substituting the values

(A’C’)² = 132 – 122

(A’C’)² = 25

A’C’ = 5 cm

Length of the new chord = 2 × 5 = 10 cm

Therefore 10 cm is the length of the new chord.