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2025 AMC 10AProblem 23P21-25~6 minPrint
Triangles: Area & PythagoreanTrigonometryApply an identity: SFFT, sum of squares, difference of cubes, VietaSet up the equation/formula and compute; no special trick needed

Triangle △ABC\triangle ABC has side lengths AB=80AB = 80 , BC=45BC = 45 , and AC=75AC = 75 . The bisector of ∠B\angle B and the altitude to side AB‾\overline{AB} intersect at point P.P. What is BPBP ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.