In your answer, you showed the same formula for (-7,7) as for (6,8). Just to be clear, the radius of a circle is
the square root of [{(the distance of 0,0 to X)squared} plus {(the distance from 0,0 to Y)squared}. Yes?

Nichalia, the radius of a circle is the distance from 0,0 to any (X,Y,) on the perimeter of the circle, or in this case (6,8) is given as a point.

In this case, it's sqrt {(x-0)^2 + (y-0)^2)}, if that's what you meant, or sqrt (6^2 + 8^2), which is 10. You should memorize the Golden Triangle ratio: 3,4, and 5 as the hypotenuse. They appear quite a bit in tests like this. 6,8, then 10 is the hypotenuse. You can save time in the test.

Yes, the formula for distance is the same. The solution is just showing that the distance from O to -7,7 is less than the distance to 6,8.

I think you missed the point she was trying to make. Your answer repeats itself for both (6,8) and (-7,7). Using only (-7,7)

Cef Usa, thanks for noticing the repeat post. Regarding missing the point, I don't see it. I was pointing out to Nichalia that many times you don't need to use the formula to compute distance or radius, if you can memorize some pythagorean triplets, like: 3, 4, 5; 6, 8, 10.

Agreed - you missed the point. In the solution given to this problem, you don't plug in the right numbers the first time.

So, we choose (7,7) because the hypotenuse of this coordinate will be close to (6,8), that's the strategy of picking the numbers?!
But in the test we may have square roots numbers which makes the question a bit complicated so is there another strategy to save time?!

The solution for the problem is still wrong, which is the point that everyone seems to be making. The math for the (6,8) coordinate displays the math for the (7,7) coordinate.