







A regular hexagon and an equilateral triangle in a circle 
20100405 

Beth pose la question : A regular hexagon and an equilateral triangle are both inscribed in the same circle so that the hexagon and the triangle share three vertices. The radius of the circle is 10cm. What is the difference between the area of the hexagon and the area of the triangle? Chris Fisher lui répond. 





Creating a triangle in a circle 
20061128 

Dirk pose la question : My daughter has a school project where she must draw a circle and then draw an equilateral triangle inside the circle. She said you have to identify six points on the circle to correctly draw the triangle. How do you accomplish this? Penny Nom lui répond. 





A regular hexagon is inscribed in a circle. 
20041208 

Abraham pose la question : A regular hexagon is inscribed in a circle. What is the ratio of the length of a side of the hexagon to the minor arc that it intercepts?
(1) pi/6
(2) 3/6
(3) 3/pi (This is the correct answer.)
(4) 6/pi
I found the length of the minor arc to be (pi)(r)/3 by doing a sixth of the circumference(2pi r).But I can't find the length of the radius to finish off the problem. If I knew the radius I would then plug it into the above and then use the radius again to be the length of the side because the triangle(one of the six of a hexagon) is equilateral. But can you show me how to get the radius to be 3? Thank you so much.
Walter Whiteley lui répond. 





Two Inscribed Trapezoids 
19980127 

James pose la question : A hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. The chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to m/n, where m and n are relatively prime positive integers. Find m+n. Haragauri Gupta lui répond. 

