Draw a tangent to the circle from C, say CT is the tangent and OT is the radius (so the lines CT and OT are perpendicular). There's a theorem which says that , from which you can find CT. Then use Pythagoras.
Is it considered to be using trigonometric ratios
if you find the mid-point of the chord AB?
Since the chord length is given as 8, half would be 4.
If not then you have two 3-4-5 triangles inside the circle.
You then have sufficient information to complete the sides of a right triangle.
And from there, use pythagoras.
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