Circumcenter & Incenter

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. It is equidistant from all three vertices of the triangle.

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Front

How do you find the Circumcenter of a triangle?

Back

To find the Circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the Circumcenter.

Front

How do you find the Incenter of a triangle?

Back

To find the Incenter, construct the angle bisectors of at least two angles of the triangle. The point where they intersect is the Incenter.

Front

What is the relationship between the Circumcenter and the circumradius?

Back

The circumradius is the radius of the circumcircle, which is the circle that passes through all three vertices of the triangle. The Circumcenter is the center of this circumcircle.

Front

What is the relationship between the Incenter and the inradius?

Back

The inradius is the radius of the incircle, which is the circle that is tangent to all three sides of the triangle. The Incenter is the center of this incircle.

Front

If a triangle has angles of 34°, 68°, and 78°, what is the measure of the angle opposite the longest side?

Back

The angle opposite the longest side is 78°.

Front

In a triangle, if the lengths of the sides are 7, 24, and 25, which point of concurrency is located inside the triangle?

Back

The Incenter is located inside the triangle.

Front

What is the significance of the Circumcenter in a right triangle?

Back

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

Front

What is the significance of the Incenter in relation to triangle area?

Back

The area of a triangle can be calculated using the formula: Area = r * s, where r is the inradius and s is the semi-perimeter of the triangle.