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AMC 10A/12A 2025 (Problem 23/12)

Triangle ABCABC has side lengths AB=80AB=80, BC=45BC=45, and AC=75AC=75. The bisector of ∠B\angle B and the altitude to side ABAB intersect at point PP. What is BPBP?
(A)  18\text{(A)}\;18(B)  19\text{(B)}\;19(C)  20\text{(C)}\;20(D)  21\text{(D)}\;21(E)  22\text{(E)}\;22