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IKMC 2013 - Grades 9-10 - Self-study Question 23

IKMC · IKMC 2013 - Grades 9-10 - Self-study

Question 23

Non-overlapping isosceles triangles share vertex O and an edge with each immediate neighbour. Their angles at O are m°,2 m°,3 m°, …, where m is a positive integer. The picture shows five triangles. What is the smallest possible m?

Diagram convention used for scoring: the triangles form a closed fan filling 360° around O, with the two sides from O equal in each triangle.

Question illustration
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