Answer: Segment XY is tangent to the circle.
===========================================================
Explanation:
If XY is tangent to the circle, then the radius ZX would be perpendicular to the tangent XY. In other words, the angle YXZ would be 90 degrees.
Furthermore, it means triangle WXY would be a right triangle.
Effectively, we need to find out if triangle WXY is a right triangle.
Recall that we can use the converse of the pythagorean theorem to find out if a triangle is a right triangle or not.
We have these side lengths of the triangle:
- XY = 9.6
- WX = WZ+ZW = 6.4+6.4 = 12.8
- YW = 16
Let's say a = 9.6, b = 12.8 and c = 16
The order of 'a' and b doesn't matter. All that matters is that c is the longest side.
Plug those values into the pythagorean theorem and simplify each side.
a^2+b^2 = c^2
(9.6)^2 + (12.8)^2 = (16)^2
92.16 + 163.84 = 256
256 = 256
We end up with a true equation, so the first equation is true for those a,b,c values. Hence, we have shown that the triangle is a right triangle, and this concludes that XY is indeed tangent to the circle.
