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MathNet 2019-part-07 — 184 problems (EN–VI) Question 68

Math Olympiad Vault · MathNet 2019-part-07 — 184 problems (EN–VI)

Question 68

The convex quadrilateral $ABCD$ is given.
$\angle BAD = \angle BCD = 120^\circ$, $\angle ACD = 80^\circ$, $BC = CD$, $O$ is the intersection point of its diagonals.
Prove, that $BO^2 = AO \cdot AC$.