Geometry Puzzle – Challenge 77

This is a great math puzzle and critical thinking challenge that is sure to get you thinking!

Geometry Puzzle – Challenge 77


What is the perimeter of the inscribed equilateral triangle, if the diameter of the circle above is 4?

A- \(4\sqrt{2}\)

B- \(4\sqrt{3}\)

C- \(6\sqrt{2}\)

D- \(6\sqrt{3}\)

E- 12

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The correct answer is D.

Draw the bisector of the angle A perpendicular to line BC.
D is the center of the circle and CD is equal to the radius. The diameter of the circle above is 4. So, CD is 2.

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Triangle CDE is a 30-60-90 degree triangle and angle DCE is 30.
Since, CD is 2 (the hypotenuse of the triangle CDE), DE is 1 and CE is \(\sqrt{3}\). Why?
Therefore, BC is \(2\sqrt{3} \) and the perimeter of the triangle ABC is
\(3 × 2\sqrt{3} = 6\sqrt{3}\)

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