Maharashtra State BoardSSC (English Medium) 8th Standard

O is Centre of the Circle. Find the Length of Radius, If the Chord of Length 24 Cm is at a Distance of 9 Cm from the Centre of the Circle. - Mathematics

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Sum

O is centre of the circle. Find the length of radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.

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Solution

Join OA.

Let the perpendicular drawn from point O to the chord AB be P.
We know that the perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, AP = `"AB"/2 = 24/2` = 12 cm

In Δ OPA,
We apply the Pythagoras theorem,

OP² + AP² = OA²

⇒ 9² + 12² = OA²

⇒ OA² = 81 +144 = 225

⇒ OA = √225 15 cm 

Hence, the radius of the circle is 15 cm.

Concept: Properties of Chord of a Circle
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Chapter 17: Circle : Chord and Arc - Practice Set 17.1 [Page 116]

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Balbharati Mathematics 8th Standard Maharashtra State Board
Chapter 17 Circle : Chord and Arc
Practice Set 17.1 | Q 3 | Page 116
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