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MathNet 2018-part-01 — 181 problems (EN–VI) Question 155

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 155

Juquinha marks points on a circle and draws triangles by joining 3 of these points. The lengths of the arcs between 2 consecutive points are equal.

a) Marking 4 points on the circle, how many triangles will he be able to draw?

b) Marking 5 points on the circle, how many equilateral triangles will he be able to draw?

c) How many right triangles will he be able to draw if he marks 6 points?