Let radius OA = OC = OD = rChord AB = 12 cmOE = OC – CE⇒ OE = r – 3AE = (1/2) AB⇒ AE = (1/2) 12 = 6 cmIn triangle AOE,OA2 = AE2 + OE2⇒ r2 = 62 + (r - 3)2⇒ r2 = 36 + r2 + 9 - 6r⇒ 6r = 45⇒ r = 7.5 cmHence, radius of circle = 7.5 cm.

Q. 63.9( 20 Votes )

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

Answer :

Let radius OA = OC = OD = r

Chord AB = 12 cm

OE = OC – CE

⇒ OE = r – 3

AE = (1/2) AB

⇒ AE = (1/2) 12 = 6 cm

In triangle AOE,

OA² = AE² + OE²

⇒ r² = 6² + (r - 3)²

⇒ r² = 36 + r² + 9 - 6r

⇒ 6r = 45

⇒ r = 7.5 cm

Hence, radius of circle = 7.5 cm.

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