An equilateral triangle is drawn with each side = 10. With the base of the triangle as one side, a square is drawn (with each side = 10) below the triangle. What is the radius of the circle on which the top tip of the triangle and the bottom two vertices of the square lie?
Height of triangle = sqrt (100-25)=sqrt(75)
Take the origin to be the bottom left point on square (1) = 0,0
Bottom right point on square (2) = 10,0
Top tip of triangle (3) = 5, 10+ sqrt(75)
Assume 5,b is the center (meaning the height of the center is "b" from the bottom side of square).
Square of Distance from center to points on square (=radius squared) = 25+b2
Square of Distance from center to top point on triangle = ((10-b) +
sqrt(75)) 2
Now solve for b.
