2214

Prove the red circle is tangent to the yellow incircle.

1713

Prove the red lines are concurrent.

1357

The ratio of the inradii is $3:2$. Prove the red shape is a rectangle.

1047

Prove the ratio of the area of the blue triangle to the area of the red triangle equals the ratio of the area of the blue incircle to the area of the red nine-point circle.

997

Prove the blue circles are tangent to each other.

369

The green tangents are parallel to the sides of the red triangle. Prove $\dfrac{p}{a}+\dfrac{q}{b}+\dfrac{r}{c}=1$.

343

Prove $r=\sqrt{ab}+\sqrt{bc}+\sqrt{ca}$.

304

Prove the red line is perpendicular to the bases of the isosceles trapezoid.

210

Prove the red line segments are congruent.

133

Given an equilateral triangle. Prove $a^2+b^2+c^2$ is constant.

121

Prove the blue angles are supplementary.

116

The red points are midpoints of sides of the black triangle. Prove the red and blue points are collinear.

86

Prove $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{2}{c}$.

63

Given a rhombus. Prove $\sqrt{a+b+R}=\sqrt{a}+\sqrt{b}+\sqrt{r}$.

50

Prove the blue line segments are congruent.

46

The gray lines are parallel to the sides of the triangle. Prove the sum of the radii of the yellow circles equals the radius of the blue circle.

3

Prove $a+b=c$.