And without the theorem about intersecting chords, you can consider the perpendicular chords to be the x and y axes, and consider the center of the circle at (a,b). It is easy to see that a=2, and using the same two right triangles you identified, with the hypotenuses of r, we can get b^2+4^2 = r^2 = (3+b)^2 + 2^2. We can solve to find out that b=.5. But the property of intersecting chords you mentioned greatly simplifies the finding that b=1/2!
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