MathDB

11

Part of 1994 Baltic Way

Problems(1)

|SA'| |SB'| = |SN|^2

Source: Baltic Way 1994

12/22/2011
Let NSNS and EWEW be two perpendicular diameters of a circle C\mathcal{C}. A line ℓ\ell touches C\mathcal{C} at point SS. Let AA and BB be two points on C\mathcal{C}, symmetric with respect to the diameter EWEW. Denote the intersection points of ℓ\ell with the lines NANA and NBNB by A′A' and B′B', respectively. Show that ∣SA′∣⋅∣SB′∣=∣SN∣2|SA'|\cdot |SB'|=|SN|^2.
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