Neither secant nor tangent pass through the center of a circle. A secant passes through one point on the circle and the tangent passes through two points on a circle.
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A line joining the centres of two tangent circles also passes through the point of tangency.
The area of S is 16 square inches.
A cord that passes through the center of a circle is a diameter of that circle. And you've probably guessed that this is the largest cord of that circle.
A chord that passes through the center of a circle is its diameter.
diameter