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

State the Perpendicular Bisector Theorem.

Back

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

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 vertices of a triangle?

Back

The Circumcenter is equidistant from all three vertices of the triangle.

Front

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

Back

The Incenter is equidistant from all three sides of the triangle.

Front

If m∠CAP = 34°, what is m∠CAB if triangle JKL is isosceles with sides JK = JL?

Back

m∠CAB = 68°.

Front

What is the formula for finding the distance from a point to a line?

Back

The distance from a point (x₀, y₀) to a line Ax + By + C = 0 is given by: Distance = |Ax₀ + By₀ + C| / √(A² + B²).

Front

What is the significance of the circumradius in a triangle?

Back

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