MathDB

2

Part of 1981 Polish MO Finals

Problems(1)

BC = XY iff tanBtanC = 3 or tanBtanC = -1.

Source: Polish MO Finals 1981 p2

8/24/2024
In a triangle ABCABC, the perpendicular bisectors of sides ABAB and ACAC intersect BCBC at XX and YY. Prove that BC=XYBC = XY if and only if tan⁡Btan⁡C=3\tan B\tan C = 3 or tan⁡Btan⁡C=−1\tan B\tan C = -1.
geometrytrigonometryperpendicular bisector