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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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.
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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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.