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

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The discussion explains the multiplication rule for segments AD and CD in a circle with diameter BE. It highlights that the circle centered at point P, with radius PA equal to PB, passes through point C, where the angle at the center is twice that at the circumference. By extending BP to form the diameter BE, the relationship AD·CD = BD·DE is established. The specific calculation shows that AD·CD equals 7, derived from the values 1 and (8-1). This illustrates the geometric principles involved in the multiplication rule within the context of circle geometry.
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[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]
 
Opalg said:
[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 !
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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