Question

The circumference of the circle D is 32 times pie and IJ bisects the sides GH and GF is the square HGFD. Which is the value of IJ?

Answer 1

Chris? What happened?

Answer 2

its not letting me log in but hld on

Answer 3

I have an answer of 13.25. Let me lay out the logic on how I got there.

Answer 4

\[Circumference = 32\pi\]
\[2\pi r = Circumference = 32 \pi = 16*2\pi\]
\[r=16\]
The square is has 2 sides equal to the radius. We know that a line bisecting the line from D to G will be:
\[\sqrt{16^{2}+16^{2}}=22.63\]
We can see that the radius touches that tangent line so we can subtract to get the remainder to G. The remainder is:
\[22.63-16 = 6.63\]
We know that the upper traingles caused by the bisecting line from D to G have 45 degree angles which means the bottom line from the midpoint of IJ to I will be equal to the remainder from D to G. The triangle from IJ to J will have the same measurements so we have 2 times that height:
\[2*6.63=13.26\]

Answer 5

Let me know if you need me to clarify any points or if you find holes in the logic.