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AMO 2027 Grades 6-7 SET 16 - Self-study Question 15

AMO · AMO 2027 Grades 6-7 SET 16 - Self-study

Question 15

a) In the following figure, there are seven points on the circumference of a circle. How many triangles can be drawn with any three points as vertices?

b) In the following figure, there are eight points on the sides of a square. How many triangles can be drawn with any three points as vertices?

**Editorial note for this self-study exercise:** Use the marked points only, counting each choice of three distinct vertices once. Three collinear points do not form a triangle. Enter (a) then (b) as integers separated by a semicolon with no spaces.

Question illustration

Question illustration