Centers of Triangles

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

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 Centroid of a triangle?

Back

The Centroid is the point where the medians of a triangle intersect. It divides each median into a ratio of 2:1.

Front

If m∠BCA is 72°, what is m∠PCA if P is on the angle bisector?

Back

m∠PCA = 36°.

Front

If BX = 2, what is BZ if Z is on the angle bisector?

Back

BZ = 2.

Front

If PY = 6 and CY = 8, what is PC if P is on the angle bisector?

Back

PC = 10.

Front

If BC = 18, what is DC if D is the midpoint of BC?

Back

DC = 9.

Front

What is the relationship between the sides of a triangle and its angle bisector?

Back

The angle bisector divides the opposite side into segments that are proportional to the adjacent sides.

Front

What is the formula for finding the length of a median in a triangle?

Back

Median length = √(2a² + 2b² - c²) / 4, where a, b, and c are the lengths of the sides.

Front

What is the significance of the circumradius in a triangle?

Back

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