Circumcenter- Part 1

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.

Front

What is the special property of the circumcenter?

Back

The circumcenter is equally distant from all three vertices of the triangle.

Front

How can you find the circumcenter of a triangle using its vertices?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle; their intersection point is the circumcenter.

Front

What is the relationship between the circumcenter and the circumcircle?

Back

The circumcenter is the center of the circumcircle, which is the circle that passes through all three vertices of the triangle.

Front

If a triangle is acute, where is the circumcenter located?

Back

In an acute triangle, the circumcenter is located inside the triangle.

Front

If a triangle is right, where is the circumcenter located?

Back

In a right triangle, the circumcenter is located at the midpoint of the hypotenuse.

Front

If a triangle is obtuse, where is the circumcenter located?

Back

In an obtuse triangle, the circumcenter is located outside the triangle.

Front

What is the formula to calculate the circumradius (R) of a triangle?

Back

The circumradius R can be calculated using the formula R = (abc) / (4K), where a, b, and c are the lengths of the sides of the triangle and K is the area of the triangle.

Front

What is the significance of the circumradius in triangle geometry?

Back

The circumradius is the radius of the circumcircle and helps in understanding the triangle's properties and relationships with other geometric figures.

Front

How do you determine the lengths of segments from the circumcenter to the vertices?

Back

The lengths from the circumcenter to each vertex are equal to the circumradius R.