There are many right triangles passing through (1,8), but using the fact that the angle in a semicircle is a right angle, x2+y2=12+82=1+64=65 is a circle passing through (1,8) where the right angle is. This circle also has its centre at the origin (0,0). The vertices of the triangle are where the circle intersects the x-axis: (-√65,0), (√65,0). The diameter (hypotenuse) has length 2√65.
But other circles pass through the same point. If the centre of the circle is (1,1), for example, the radius is 7, making the circle: (x-1)2+(y-1)2=49. The diameter (hypotenuse) intersects y=1 when x-1=7, x=8 and x-1=-7, x=-6. The length of the hypotenuse is 14. The vertices are (1,8), (-6,1) and (8,1).
We can move the centre of the circle closer to (1,8) and this shortens the hypotenuse. For example, if the centre of the circle is at (1,7), the circle is (x-1)2+(y-7)2=1 and hypotenuse=2.