yes a diameter passes through the center of a circle
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Yes. The perpendicular bisector of a chord forms a radius when extended to the centre of the circle and a diameter when extended beyond the centre to the opposite point on the circumference.
This is not possible, since the point (4,6) lies inside the circle : X2 + Y2 = 16 Tangents to a circle or ellipse never pass through the circle
No
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Yes