What is the Multiplication Rule for AD and CD in a Circle with a Diameter BE?

[Albert1]

View attachment 2739

 

[Opalg]

[sp]The circle centred at $P$ with radius $PA = PB$ passes through $C$ (angle at centre = twice angle at circumference). Extend $BP$ to form a diameter $BE$ of the circle. Then $AD\cdot CD = BD\cdot DE = 1\cdot (8-1) = 7$.[/sp]

 

[Albert1]

[sp]The circle centred at $P$ with radius $PA = PB$ passes through $C$ (angle at centre = twice angle at circumference). Extend $BP$ to form a diameter $BE$ of the circle. Then $AD\cdot CD = BD\cdot DE = 1\cdot (8-1) = 7$.[/sp]

very good !