MathDB
vertors OI = OA_1+OB_1 + OC_1, arc midpoints

Source: 1991 Greece MO Grade XII p2

September 6, 2024
geometrycircumcirclevectorarc midpoint

Problem Statement

Let OO be the circumcenter of triangle ABCABC and let A1,B1,C1A_1,B_1,C_1 be the midpoints of arcs BC,CA,ABBC, CA,AB respectively. If II is the incenter of triangle ABCABC, prove that OI→=OA1→+OB1→+OC1→.\overrightarrow{OI}= \overrightarrow{OA_1}+ \overrightarrow{OB_1}+ \overrightarrow{OC_1}.
Back to ProblemsView on AoPS