Geometry Puzzle – Challenge 77
This is a great math puzzle and critical thinking challenge that is sure to get you thinking!
Challenge:
What is the perimeter of the inscribed equilateral triangle, if the diameter of the circle above is 4?
A- 4√2
B- 4√3
C- 6√2
D- 6√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.
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 √3. Why?
Therefore, BC is 2√3 and the perimeter of the triangle ABC is
3×2√3=6√3
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