I'm sorry my semi circle isn't drawn very well, but it is meant to be a semi circle.

this is what I did, could you please tell me where I went wrong?

Because the distance from the point of (0,0) to both the bottom right and bottom left point is 10 units, so I assumed that the distance from that point to any point on the semi circle would be 10 units.

From here, I used the distance formula (d=square root of (x2-x1)^2+(y2-y1)^2) putting in (0-s)^2+(0-8)^2 and putting in "10" as d.

So:

10=SQUAREROOT[(0-s)^2+(0-8)^2]

From here I solved until I got d=-2.

But the answer in the back of the book is "6".

Could you please tell me where I went wrong in the process and how to fix it?

If I made a mistake in solving for d and I did everything else right can you show me how to accurately solve for d?

Thank you very much!