In the bottom diagram

\[xy=d^2\]

To prove this notice that AC is a diamter so ABC is a right angle.

\[tan \theta = \frac{d}{y} = \frac{x}{d} \]

Hence

\[xy=d^2\]

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In the diagram below the diameter AC bisects the chord BD at right angles.

In the bottom diagram

To prove this notice that AC is a diamter so ABC is a right angle.

Hence

In the bottom diagram

\[xy=d^2\]

To prove this notice that AC is a diamter so ABC is a right angle.

\[tan \theta = \frac{d}{y} = \frac{x}{d} \]

Hence

\[xy=d^2\]