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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. - SSC (English Medium) Class 8 - Mathematics

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Question

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.

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.

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 17: Circle : Chord and Arc
Practice Set 17.1 | Q: 3 | Page no. 116
Solution 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. Concept: Properties of Chord of a Circle.
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