MathDB
concurrency wanted, <BAD = <DBC, <DAC = <BCD

Source: Switzerland - Swiss MO 2018 p4

July 14, 2020
geometryconcurrentequal angles

Problem Statement

Let DD be a point inside an acute triangle ABCABC, such that ∠BAD=∠DBC\angle BAD = \angle DBC and ∠DAC=∠BCD\angle DAC = \angle BCD. Let PP be a point on the circumcircle of the triangle ADBADB. Suppose PP are itself outside the triangle ABCABC. A line through PP intersects the ray BABA in XX and ray CACA in YY, so that ∠XPB=∠PDB\angle XPB = \angle PDB. Show that BYBY and CXCX intersect on ADAD.
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