I was reviewing when I came upon a problem that requires me to construct a line with length $\sqrt7R$, where $R$ is the radius of a given circle.
I can do a line with a $\sqrt7$ unit length just fine but this one just confuses me.
Hope you guys can point me in the right direction.
Hint: think Pythagoras and remember:
$$1^2 + 1^2 = (\sqrt 2)^2$$ $$(\sqrt 2)^2 + 1^2 = (\sqrt 3)^2$$ $$(\sqrt 3)^2 + 2^2 = (\sqrt 7)^2$$
Using a straightedge and a compass you can bisect (and double) line segments and construct right angles.
If you're required to start from a circle (without that centre being marked), then stay calm, draw any two non parallel chords. The perpendicular bisectors of these chords will meet at the centre, and once you've found the centre you can immediately draw the diameter line (and you know both radius and diameter).