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MathNet 2008-part-03 — 165 problems (EN–VI) Question 111

Math Olympiad Vault · MathNet 2008-part-03 — 165 problems (EN–VI)

Question 111

Three distinct diameters are drawn on a unit circle such that chords are drawn as shown in Figure 2. If the length of one chord is $\sqrt{2}$ units and the other two chords are of equal lengths, what is the common length of these chords?

Question illustration
Figure 2: Problem 60.1.