LETABCBE A FIXED TRIANGLE. POINTDIS AN ARBITRARY POINT ON THE SIDEB...
4. LetABCbe a fixed triangle. PointDis an arbitrary point on the sideBC. PointP is fixed onAD. Thecircumcircle of triangleBP DmeetsABatEdistinct fromB. PointQvaries onAP. LetBQandCQmeet the circumcircles of trianglesBP D,CP Drespectively atF, Zdistinct fromB, C. Prove that thecircumcircleEF Zis through a fixed point distinct fromEand this fixed point is on the circumcircle oftriangleCP D.Kostas Vittas