# A circle and a pentagon

Geometry Level 3

Pictured here is a $${\color{Blue} \text{regular pentagon}}$$ which has one vertex on a $${\color{Purple} \text{unit circle}}$$, and the $${\color{Green} \text{green line segments}}$$ connect vertices of the pentagon:

What is the length of the $${\color{Orange} \text{orange line segment}}$$?

Provide your answer to 3 decimal places. If you think not enough information is given, submit -1 as your answer.

Note: The circle isn't necessarily tangent to any of the line segments drawn.

×