## Circle Properties

- Triangles with two radii sides are isosceles, and if a chord is also a radius, the triangle is equilateral.
- Central angles have the same measure as the arc they intercept, and a diameter forms a 180-degree central angle, dividing the circle into two semicircles.
- Inscribed angles are half the measure of the arc they intercept, and angles inscribed in a semicircle are right angles.
- Equal chords in the same circle intercept arcs of equal length, and inscribed angles intercepting the same arc or chord are equal.
- A tangent line touches the circle at only one point and is perpendicular to the radius at the point of tangency.

**FAQ:** How do we know that O is the origin?

**Answer:** On the GRE itself, the origin will be labeled as such. You will see something like "...at origin O" in the question stem. The origin is *traditionally* represented with "O," which is the assumption made here. But the exam will note the origin specifically if you need to know what it is.

**FAQ:** Didn't the previous lesson say that an arc had to be named with three points?

**Answer**: The lesson on Circles does say that an arc will *usually* be named with three points on the exam, for the sake of clarity. But this is not a requirement in geometry. In the practice problem at 3:30, the context makes it extremely clear that arc AB refers to the short distance along the edge of the circle between points A and B.