An obtuse triangle and its circumcenter

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In summary, the conversation is about trying to prove that the circumcenter of an obtuse triangle lies outside of the triangle. The person has been unable to create a synthetic proof but has observed that it works on GSP. They mention using III. 20 and that the angle BOC is 2 times the size of angle A.
  • #1
chaotixmonjuish
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I'm having a bit of difficulty proving this, but this is what I have so far:

Let a circle with a center O and a diameter AD. Let triangle ABC be a triangle with all points on the circle and angle A be greater than 90. Because of III. 20, and BOC is 2 times the size of angle A.

This is all I can reason through. I can see that it works on GSP, but I haven't been able to create a synthetic proof.
 
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  • #2
Could be my English fails me, but I have no idea what you are trying to prove.
 
  • #3
I'm trying to prove that the circumcenter of an obtuse triangle lies outside of the triangle.
 

FAQ: An obtuse triangle and its circumcenter

What is an obtuse triangle?

An obtuse triangle is a type of triangle in which one of the angles measures more than 90 degrees.

What is the circumcenter of an obtuse triangle?

The circumcenter of an obtuse triangle is the point where the perpendicular bisectors of the sides of the triangle intersect. It is also the center of the circle that passes through all three vertices of the triangle.

How is the circumcenter of an obtuse triangle found?

The circumcenter of an obtuse triangle can be found by constructing the perpendicular bisectors of the sides of the triangle and finding the point of intersection. Alternatively, it can also be found by using the coordinates of the three vertices of the triangle and using a formula to calculate the circumcenter.

What are the properties of the circumcenter of an obtuse triangle?

The circumcenter of an obtuse triangle is equidistant from all three vertices of the triangle, and the distance from the circumcenter to each vertex is equal to the radius of the circumcircle. It also lies outside the triangle if the triangle is obtuse.

How is the circumcenter of an obtuse triangle useful?

The circumcenter of an obtuse triangle is useful in geometry and trigonometry for various calculations and constructions, such as finding the center of a circle that passes through three given points or constructing a circle that is tangent to all three sides of an obtuse triangle.

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