MathDB
2022 Team P15

Source:

February 28, 2022
team

Problem Statement

Let ABCABC be a triangle with AB=5,BC=13,AB = 5, BC = 13, and AC=12AC = 12. Let DD be a point on minor arc ACAC of the circumcircle of ABCABC (endpoints excluded) and PP on BC‾\overline{BC}. Let B1,C1B_1, C_1 be the feet of perpendiculars from PP onto CD,ABCD, AB respectively and let BB1,CC1BB_1, CC_1 hit (ABC)(ABC) again at B2,C2B_2, C_2 respectively. Suppose that DD is chosen uniformly at random and AD,BC,B2C2AD, BC, B_2C_2 concur at a single point. Compute the expected value of BP/PCBP/PC.
Proposed by Grant Yu
Back to ProblemsView on AoPS