2152

Prove the red point trisects the blue line segment.

2108

The blue point is the centroid of the yellow triangle. Prove the red points are collinear.

2046

The base of the blue triangle is the arithmetic mean of the other two sides. The blue point is the centroid of the blue triangle. The green point is the orthocenter of the green triangle. Prove the red, blue, and green points are collinear.

1724

The yellow triangles are similar. Prove the blue and red triangles have the same centroid.

1481

The green points are the centroids of the green triangles. The yellow points are the centroids of the yellow triangles. Prove the green and yellow points are concyclic.

1306

The green triangles are equilateral. Prove the red and yellow triangles have the same centroid.

1212

The blue shape is a rhombus. The green point is the centroid of the green triangle. Prove the red and green points are collinear.

1206

Prove the green and blue triangles have the same centroid.

1152

The green and blue points are the centroids of the green and blue triangles. Prove the red line segments are congruent.

1118

Point $G$ is the centroid of the triangle. Prove $\dfrac{1}{GA}+\dfrac{1}{GB}=\dfrac{1}{GC}$.

1117

The red points are the midpoints of the sides of the black triangle. Prove the yellow area equals the green area and the centroid of the black triangle is the midpoint of the centroids of the yellow and green triangles.

1104

Sqaures are constructed on the sides of a triangle. Prove blue area equals the yellow area and all three triangles have the same centroid.

1099

The blue point is the centroid of the blue triangle. The green point is the centroid of the green triangle. The yellow points are the centroids of the yellow triangles. Prove the red shape is a parallelogram whose area is $2/9$ the area of the pentagon.

956

The red point is the centroid of the triangle. Prove the color points are concyclic.

881

Prove the red triangle, blue triangle, and green quadrilateral all have the same centroid.

863

Prove the blue and green triangles have the same centroid.

802

The red point is the centroid of the red triangle. The green point is the centroid of the green triangle. The blue points are the midpoints of the diagonals of the quadrilateral. Prove the blue and yellow points are collinear.

786

The blue point is the centroid of the black triangle. The red shape is a parallelogram. Prove the green line segment is trisected by the sides of the triangle.

766

The red points are the centroids of the green and yellow triangles. The blue points are the orthocenters of the green and yellow triangles. Prove the red and green quadrilaterals are similar.

530

Prove the red angles are congruent if and only if the blue angles are congruent.