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0172 geo inequalities 1st edition Round 7 p2

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May 9, 2021
geometry1st edition

Problem Statement

Consider the circles ω\omega, ω1\omega_1, ω2\omega_2, where ω1\omega_1, ω2\omega_2 pass through the center OO of ω\omega. The circle ω\omega cuts ω1\omega_1 at A,EA, E and ω2\omega_2 at C,DC, D. The circles ω1\omega_1 and ω2\omega_2 intersect at OO and MM. If ADD cuts CECE at BB and if MN⊥BOMN \perp BO, (N∈BON \in BO) prove that 2MN2≤BM⋅MO2MN^2 \le BM \cdot MO.
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