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Two chords AB and CD of lengths 4 cm and 10 cm respectively are parallel and are on the same side of the centre O of a circle. If the distance between chords is 3 cm, then what is the diameter of the circle? |
\(\sqrt {29}\) 2\(\sqrt {29}\) 3\(\sqrt {29}\) 4\(\sqrt {29}\) |
2\(\sqrt {29}\) |
Let OP = x cm In ΔBQO: (BO)2 = (BQ)2 + (QO)2 = (2)2 + (3 + x)2 In ΔCPO: (CO)2 = (CP)2 + (PO)2 = (5)2 + (x)2 Hypotenuse of ΔBQO and ΔCPO are same = radius Therefore, ⇒ (2)2 + (3 + x)2 = (5)2 + (x)2 ⇒ 4 + 9 + x2 + 6x = 25 + x2 ⇒ 6x = 12 ⇒ x = 2 (CO)2 = (CP)2 + (PO)2 = (5)2 + (2)2 = 25 + 4 = 29 OC = \(\sqrt {29}\) = radius diameter = 2 × OC = 2\(\sqrt {29}\)cm |
