2194

Prove the red points are concyclic.

2159

Prove the red lines are perpendicular.

2127

Prove the difference of the green angles equals the difference of the blue angles equals half the difference of the red angles.

2123

Prove the red lines are parallel.

2071

The blue and yellow circles are congruent. Prove the red points are concyclic.

2035

Prove each of the red midlines bisects the blue line segment.

1919

Prove the red lines are perpendicular.

1719

The blue lines are the angle bisectors of the yellow quadrilateral. Prove the red shape is a rectangle.

1579

Prove $ac = bd$.

1475

Prove the area of the quadrilateral is $\frac{1}{2}(ac+bd)$.

1183

Prove $ap+cr=bq+ds$.

953

Prove $\left( \dfrac{r}{R+d} \right)^2 + \left( \dfrac{r}{R-d} \right)^2 = 1$

938

Prove the area of the quadrilateral is $\dfrac{(ab+cd)(ac+bd)(ad+bc)}{16R^2}$

928

Prove the red line segments are congruent.

781

Prove the red lines are concurrent.

756

Prove the blue lines are parallel.

725

Prove the red points are collinear.

722

The red point is the midpoint of a side of the quadrilateral. Prove the blue and red points and concyclic.

710

Prove the red shape is a rectangle.

706

The red points are midpoints of sides and diagonals of a cyclic quadrilateral. Prove the green point is the orthocenter of the blue triangle.