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right angle and coplanar points wanted

Source: Polish MO Recond Round 1985 p6

September 9, 2024
geometry3D geometryright angle

Problem Statement

There are various points in space A,B,C0,C1,C2 A, B, C_0, C_1, C_2 , with ∣ACi∣=2∣BCi∣ |AC_i| = 2 |BC_i| for i=0,1,2 i = 0,1,2 and ∣C1C2∣=43∣AB∣ |C_1C_2|=\frac{4}{3}|AB| . Prove that the angle C1C0C2 C_1C_0C_2 is right and the points A,B,C1,C2 A, B, C_1, C_2 lie on one plane.
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