MathDB

24

Part of 2022 BMT

Problems(1)

BMT 2022 Guts #24

Source:

8/31/2023
Let △BCD\vartriangle BCD be an equilateral triangle and AA be a point on the circumcircle of △BCD\vartriangle BCD such that AA is on the minor arc BDBD. Then, let PP be the intersection of AB‾\overline{AB} with CD‾\overline{CD}, QQ be the intersection of AC‾\overline{AC} with DB‾\overline{DB}, and RR be the intersection of AD‾\overline{AD} with BC‾\overline{BC}. Finally, let XX, YY , and ZZ be the feet of the altitudes from PP, QQ, and RR, respectively, in triangle △PQR\vartriangle PQR. Given BQ=3−5BQ = 3 -\sqrt5 and BC=2BC = 2, compute the product of the areas [△XCD]⋅[△YDB]⋅[△ZBC][\vartriangle XCD] \cdot [\vartriangle Y DB] \cdot [\vartriangle ZBC].
geometry