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Samantha and Shummus both realised that in order to create a triangle with a right angle, the band had to go through the centre of the circle. Shummus writes:
I noticed that the bands had to be started in the centre.Xianglong Ni notes that:
If we have 9 points on the circle then you can't create a right-angle using the points. This is so because a right angle is inscribed in a semicircle; It is facing a diameter. But you can only create a diameter when there is an even amount of points on the circle. If the number of points on the circle is even then yes. If the number is odd then no.
Rachel from Newstead sent us a few diagrams to illustrate examples of right-angled triangles in circles with an even number of points.