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another easy problem

Source: II Caucasus Mathematical Olympiad

March 20, 2018
algebra

Problem Statement

Two points AA and BB lie on two branches of hyperbola given by equation y=1xy=\frac1x. Let AxA_x and AyA_y be projections of AA onto coordinate axis, similarly, let BxB_x and ByB_y be projections of BB onto coordinate axis. Prove that triangles ABxByAB_xB_y and BAxAyBA_xA_y have equal areas.
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