MHB Geometry: proving two angles are equal

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In geometry, proving two angles are equal often involves understanding the properties of circles. When considering a circle with diameter OC, the angles subtended by the endpoints of the diameter at any point on the circle are right angles. This means that if two angles are formed by lines intersecting at points on the circumference, and one of those lines is a diameter, the angles are equal. Utilizing the inscribed angle theorem can also aid in establishing angle equality. Understanding these principles is crucial for solving related geometric problems effectively.
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can some one show me how to work this out
 

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Re: geomertry

Hint: What can you say about the circle that has $OC$ as a diameter?
 

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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