How many points can be drawn on a circle such that each two adjacent points are at the same distance, and each three adjacent points form an angle of \(7^o 30'\).
Student tip
You need to recall on the properties of inscribed angles in a circle.
Solution
Let A, B and C be the three consecutive points on the circle. Then, we have that the inscribed angles ACB and BAC have \(7^o 30'\) each, since the distance between A and B is equal to the distance between B and C. According to the relationship between central angle and inscribed angle, we have that the central angle that corresponds to the inscribed angle ACB is \(2 \cdot 7^o 30' = 15^o\). The same stands for the central angle that corresponds to the arc between any two adjusted points. Since, \(360^o / 15^o = 24\), we have that there are 24 points on a circle with the given property.
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