MathDB

7

Part of 2015 NZMOC Camp Selection Problems

Problems(1)

circumcenter of APD is foot of perpendicular from A on BC, NP = NQ, cyclic BPQC

Source: 2015 NZOMC Camp Selections p7

1/10/2021
Let ABCABC be an acute-angled scalene triangle. Let PP be a point on the extension of ABAB past BB, and QQ a point on the extension of ACAC past CC such that BPQCBPQC is a cyclic quadrilateral. Let NN be the foot of the perpendicular from AA to BCBC. If NP=NQNP = NQ then prove that NN is also the centre of the circumcircle of APQAPQ.
geometrycircumcirclecyclic quadrilateralCircumcenter