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0653 geometric inequality with areas 6th edition Round 5 p3

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May 3, 2021
geometrygeometric inequality6th edition

Problem Statement

Let ABCABC be a triangle, and let ABB2A3ABB_2A_3, BCC3B1BCC_3B_1 and CAA1C2CAA_1C_2 be squares constructed outside the triangle. Denote with SS the area of the triangle ABCABC and with s the area of the triangle formed by the intersection of the lines A1B1A_1B_1, B2C2B_2C_2 and C3A3C_3A_3. Prove that s≤(4−23)Ss \le (4 - 2\sqrt3)S.
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