MHB What Is $\angle ADB$ in a Plane with Given Side Lengths?

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The problem involves a geometric configuration with equal side lengths of 10 for segments AB, BC, CA, and CD, while segment AD measures 11. Participants discuss methods to determine the angle ADB using the given lengths. Various approaches, including the Law of Cosines and triangle properties, are explored to find the angle. The challenge lies in the non-standard triangle formed by the points. Ultimately, the goal is to calculate the precise measure of angle ADB based on the provided dimensions.
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In a plane we have :$\overline {AB}=\overline {BC}=\overline {CA}=\overline {CD}=10$ and $\overline {AD}=11$

find :$\angle ADB=?$
 
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johng said:
Simple solution:
very nice!
 

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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