Find the Diameter.

Since hypotenuse $DB = 7.81$ and leg $AB = 6$ , using the pythagorean theorem, we can figure out the value of leg $DA$ , which is $DA= \sqrt { DB^2 + AB^2 } = \sqrt {7.81^2 + 6^2} ≈ 4.99961$ Now that we know the value of $DA$ , we can easily find the diameter of circle $EFG$ , as $DA = BE$ and $EBG$ = $2BE = 2DA = 2(5)$ , which is equal to $10$ . So, the diameter of circle $EFG = 10$ .