1250

Given a regular heptagon. Prove $\dfrac{a^2}{b^2}+\dfrac{b^2}{c^2}+\dfrac{c^2}{a^2}=6$ and $\dfrac{b^2}{a^2}+\dfrac{c^2}{b^2}+\dfrac{a^2}{c^2}=5$.

1061

Given a regular heptagon. Prove the red circles are tangent to each other.

930

Given a regular heptagon. Prove the red lines are parallel.

909

Given a regular heptagon. Prove the blue area equals the red area.

787

Given a regular heptagon. Prove the sum of the red line segments equals the the blue line segment.

384

Prove the red line is parallel to a side of the regular heptagon.

311

Given a heptagonal triangle (with angles in the ratio $1:2:4$). Prove the green incentral triangle is isosceles.

34

Given a regular heptagon. Prove $a+b=c$.

7

Given a regular heptagon. Prove $\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{1}{c}$.

4

All the line segments are congruent. Find $x$.