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MB/ MC+ ND/NC >1, rectangle ABCD

Source: 1988 Greece MO Grade XI p3

September 7, 2024
geometryrectanglegeometric inequality

Problem Statement

Bisectors of ∠BAC\angle BAC, ∠CAD\angle CAD in a rectangle ABCDABCD , intersect the sides BCBC, CDCD at points MM and NN resp. Prove that (MB)(MC)+(ND)(NC)>1\frac{(MB)}{(MC)}+\frac{(ND)}{(NC)}>1
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