MathDB

2021.10.3

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

CX=CY wanted, intersecting circles, # (2021 Kyiv City MO 10.3 11.3)

Source:

2/15/2021
Circles ω1\omega_1 and ω2\omega_2 with centers at points O1O_1 and O2O_2 intersect at points AA and BB. A point CC is constructed such that AO2CO1AO_2CO_1 is a parallelogram. An arbitrary line is drawn through point AA, which intersects the circles ω1\omega_1 and ω2\omega_2 for the second time at points XX and YY, respectively. Prove that CX=CYCX = CY.
(Oleksii Masalitin)
geometrycirclesequal segmentsparallelogram