Question

The circumference of the circle D is and IJ bisects the sides GH and GF is the square HGFD. Which is the value of IJ?
http://assets.openstudy.com/updates/attachments/4e286f130b8b3d38d3b8eee3-chris%2Bparks-1311272737039-ifd.gif

Answer 1

http://assets.openstudy.com/updates/attachments/4e286f130b8b3d38d3b8eee3-chris%2Bparks-1311272737039-ifd.gif

Answer 2

if GI=FI and HJ=GJ
then IJ=1/2HF

Answer 3

What is the diameter?

Answer 4

IJ would be easy to calculate if the diameter is known.

Answer 5

reason behind @Raya_Atour 's statement: Midline theorem, which states that "the line connecting the midpoints of the legs of an isosceles or equilateral triangle is parallel to the base and is half as long."

Answer 6

We don't need no theorems. Since that figure is square and intersection points are half way, there is a right triangle with legs = 1/2 the side of square = 1/2 radius. So, simply use pythagorean theorem to calculate hypotenuse, which is the side IJ.

Answer 7

Right triangle is IJG