\[xy=d^2\]
To prove this notice that AC is a diamter so ABC is a right angle.
\[tan \theta = \frac{d}{y} = \frac{x}{d} \]
Hence
\[xy=d^2\]
Proof of Diameter Chord Formula
In the diagram below the diameter AC bisects the chord BD at right angles.
To prove this notice that AC is a diamter so ABC is a right angle.
Hence
To prove this notice that AC is a diamter so ABC is a right angle.
Hence