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# 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. - ICSE Class 10 - Mathematics

ConceptChord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)

#### 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,
OA2 = OC2 + AC2  (By Pythagoras theorem)
⇒ AC2 = (17)2 - (8)2 = 225
⇒ AC = 51 cm
∴ AB = 2 AC = 2 × 15 = 30 cm

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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).
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