Circumcenter & Incenter

Front

What is the Circumcenter of a triangle?

Back

The Circumcenter is the point of concurrency of the three perpendicular bisectors of a triangle.

Front

How can you find the length of a segment using the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment.

Front

What is the Incenter of a triangle?

Back

The Incenter is the point of concurrency of the three angle bisectors of a triangle.

Front

How do you find the Inradius of a triangle?

Back

The Inradius can be found using the formula: r = A/s, where A is the area of the triangle and s is the semi-perimeter.

Front

What is the relationship between the circumradius and the sides of a triangle?

Back

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

Front

What theorem can be used to find the lengths of segments in a right triangle?

Back

The Pythagorean Theorem can be used, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Front

What is the formula for the area of a triangle using the inradius?

Back

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

Front

What is the significance of the circumcircle of a triangle?

Back

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

Front

How do you determine the coordinates of the circumcenter in a coordinate plane?

Back

The circumcenter can be found by solving the equations of the perpendicular bisectors of the sides of the triangle.

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter (s) is half the sum of the lengths of the sides of the triangle, calculated as s = (a + b + c)/2.