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EQ = FQ iff BP = CP

Source: Indonesia MO (INAMO) 2015 P6

September 14, 2018
geometryequal segmentscircumcircleperpendicular

Problem Statement

Let ABCABC be an acute angled triangle with circumcircle OO. Line AOAO intersects the circumcircle of triangle ABCABC again at point DD. Let PP be a point on the side BCBC. Line passing through PP perpendicular to APAP intersects lines DBDB and DCDC at EE and FF respectively . Line passing through DD perpendicular to BCBC intersects EFEF at point QQ. Prove that EQ=FQEQ = FQ if and only if BP=CPBP = CP.
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