Math CentralQuandaries & Queries


Question from Heidemarie, a student:

The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle.


circle, triangle and hexagon

$PR$ is perpendicular to $QS.$

What is the measure of the angle $SPQ?$

What is the measure of the angle $QSP?$

The result follows for knowing that in a "30, 60 90" triangle the ratio of the side lengths is $1:2:\sqrt{3}.$


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