Question

GRE Review: Circles

Answer 1

\({\bf{Basics:}}\)

> a triangle made by connecting 1) the center and 2) two points on the circle, is isosceles, since the radii act as two equal side. as a reminder, an isosceles triangle creates two equal angles (not between the congruent sides)



> circumference = pi*d
> area = pi*r^2
> all angles/arcs in a circle add up to 360, just be careful not to duplicate/double-count any overlapping regions of the arcs/angles

Answer 2

> arcs: for angle x on the center of the circle, arc = (x/360) * 2*pi*r
if you forget this, remember it's the fraction of the whole circle represented by the angle, times the circumference
> sectors: for angle x on the center of the circle, sector = (x/360) * pi*r^2
if you forget this, remember i'ts the fraction of the whole circle represented by the angle ,times the area

this only works if the angle x is on the center, otherwise you have some strategies
1. you may be able to find what the center angle is
2. you may be able to break down the sector into other shapes and take the area that way

Answer 3

one last thing, if a tangent is drawn (a line that only intersects the circle once, on the outer edge), the angle formed between the radius and the tangent is 90 degrees

Answer 4

Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the 19th edition Barron's prep book for the new GRE.