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(a) Let AABC be an acute triangle with orthocentre H and circumcentre O. Let A' be the midpoint of BC and let D be the

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(a) Let AABC be an acute triangle with orthocentre H and circumcentre O. Let A' be the midpoint of BC and let D be the foot of the altitude from A. Suppose that HOA'D is a rectangle with HO = 11 and OA' = 5. What is the length of BC? (b) Prove that if AABC is acute and has the property that its Euler line is parallel to BC, then tan B tan C = 3

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