#### Question

The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

#### Solution

Let AB be the chord and O be the centre of the circle.

Let OC be the perpendicular drawn from O to AB.

We know, that the perpendicular to a chord, from the centre of a circle, bisects the chord.

∴ AC = CB

In ∆OCA,

OA^{2} = OC^{2} + AC^{2} (By Pythagoras theorem)

⇒ AC^{2} = (17)^{2} - (8)^{2} = 225

⇒ AC = 51 cm

∴ AB = 2 AC = 2 × 15 = 30 cm

Is there an error in this question or solution?

Solution The Radius of a Circle is 17.0 Cm and the Length of Perpendicular Drawn from Its Centre to a Chord is 8.0 Cm. Calculate the Length of the Chord. Concept: Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof).