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"Triangles in a semicircle": ABC is a right (90 degree) angle?

Link

https://gre.magoosh.com/questions/94

 

Question

How do we know that angle ABC is a right angle?

 

Answer

There are two things we need to know to understand the right angle 1. We are told O is the center, and any line that goes from the center of a circle to the circle edge is a radius.

2. When you have an inscribed angle in a triangle that connects to the diameter, that inscribed angle is always 90 degrees. The related lesson about circle properties linked below covers this topic in more detail.

 

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