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MA/ AA_1+ MB/ BB_1> 2 MG/ GG_1

Source: 1987 Greece MO Grade XI p4

September 6, 2024

geometrygeometric inequality

Problem Statement

Let

A,B

be two points interior of circle

C(O,R)

and

M

a point on the circle. Let

A_1,B_1

be the intersections of the circle with lines

MA

,

MB

respectively. Let

G

be the midpoint of

AB

and

G_1= C\cap MG

. Prove that

\frac{MA}{AA_1}+ \frac{MB}{BB_1}> 2\frac{MG}{GG_1}

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