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Circle Properties

This content delves into advanced concepts of circle geometry, focusing on angles within circles, their properties, and their implications for solving GRE geometry problems.
  • 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.
Central and Inscribed Angles
Properties of Central Angles
Understanding Inscribed Angles
Tangent Lines and Circles

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 " 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.