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O is the centre of an ellipse with major axis AB and minor axis CD. F is a focus. If OF = 6 and the inscribed circle of triangle OCF has diameter 2, find the product (AB)(CD).
- 65
- 45
- 55
- 75
Correct answer: 65
Solution
With c = 6, OC = b, CF = a, inradius (b + 6 - a)/2 = 1; using a² = b² + 36 gives a = 6.5, b = 2.5, so AB*CD = 2a*2b = 13*5 = 65.
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