Let distance OC = 8 cmChord AB = 30 cmDraw OCABTherefore,OC bisects AB at CAC = (1/2) AB⇒ AC = (1/2) 30⇒ AC = 15 cmIn triangle OCA,OA2 = OC2 + AC2⇒ OA2 = 82 + 152⇒ OA2= 64 + 225⇒ OA2= 289⇒ OA = 17 cmHence, radius of the circle = 17 cm.

Q. 34.0( 19 Votes )

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Class 9th RS Aggarwal & V Aggarwal - Mathematics 11. Circles

Answer :

Let distance OC = 8 cm

Chord AB = 30 cm

Draw OCAB

Therefore,

OC bisects AB at C

AC = (1/2) AB

⇒ AC = (1/2) 30

⇒ AC = 15 cm

In triangle OCA,

OA² = OC² + AC²

⇒ OA² = 8² + 15²

⇒ OA²= 64 + 225

⇒ OA²= 289

⇒ OA = 17 cm

Hence, radius of the circle = 17 cm.

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