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With the triangle on the middle

2019-11-02T15:13:46.377Z


Three randomly selected points on a circle form a triangle. What is the probability that the center of the circle lies in the triangle?



It is always exciting when two mathematical subjects come together. For the following problem these are the geometry and the probability calculus. This makes the task clear on the one hand - but also quite tricky.

Given is a circle. On this circle, three points are randomly selected and connected. This creates a so-called Sehnendreieck. The corners of this triangle are on the circle.

We also record the center of the circle. This can be enclosed by the three sides, but also outside the triangle - see following drawing.

MIRROR ONLINE

What is the probability that the center of the circle lies within the triangle or on one of its three sides? (Note: the three points on the circle are randomly chosen.)

Source: spiegel

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