MathDB

5

Part of 2015 USAJMO

Problems(1)

Points with equal angles

Source: 2015 USAJMO problem 5

4/29/2015
Let ABCDABCD be a cyclic quadrilateral. Prove that there exists a point XX on segment BD‾\overline{BD} such that ∠BAC=∠XAD\angle BAC=\angle XAD and ∠BCA=∠XCD\angle BCA=\angle XCD if and only if there exists a point YY on segment AC‾\overline{AC} such that ∠CBD=∠YBA\angle CBD=\angle YBA and ∠CDB=∠YDA\angle CDB=\angle YDA.
USA(J)MOUSAJMOgeometrycyclic quadrilateral2015 USAJMOsimilar trianglestrigonometry