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2.1

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 2.1 OM >= R , S_bS_c = S_aS_b+S_aS_c

Source:

6/6/2020
Let ABCABC be an equilateral triangle with circumcircle of center OO and radius RR. Point MM is exterior to the triangle such that SbSc=SaSb+SaScS_bS_c = S_aS_b+S_aS_c, where Sa,Sb,ScS_a, S_b, S_c are the areas of triangles MBC,MCA,MABMBC,MCA,MAB respectively. Prove that OM≥ROM \ge R.
Nguyễn Tiến Lâm
area of trianglegeometric inequalitygeometryEquilateralcircumcircleareas