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Geometry Mathley 15.4 fixed point lies on circumcircle

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June 14, 2020
geometryfixedFixed pointcircumcircle

Problem Statement

Let ABCABC be a fixed triangle. Point DD is an arbitrary point on the side BCBC. Point PP is fixed on ADAD. The circumcircle of triangle BPDBPD meets ABAB at EE distinct from BB. Point QQ varies on APAP. Let BQBQ and CQCQ meet the circumcircles of triangles BPD,CPDBPD, CPD respectively at F,ZF,Z distinct from B,CB,C. Prove that the circumcircle EFZEFZ is through a fixed point distinct from EE and this fixed point is on the circumcircle of triangle CPDCPD.
Kostas Vittas
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