MathDB

4

Part of 2015 Dutch BxMO/EGMO TST

Problems(1)

dutch angle chasing for TST, 2 circles and angle bisector related

Source: 2015 Dutch BxMO / EGMO TST p4

9/19/2018
In a triangle ABCABC the point DD is the intersection of the interior angle bisector of ∠BAC\angle BAC and side BCBC. Let PP be the second intersection point of the exterior angle bisector of ∠BAC\angle BAC with the circumcircle of ∠ABC\angle ABC. A circle through AA and PP intersects line segment BPBP internally in EE and line segment CPCP internally in FF. Prove that ∠DEP=∠DFP\angle DEP = \angle DFP.
geometrycircumcircleequal anglesAngle Chasingangle bisector