What does the angle subtended by an arc at the center of a circle equal compared to the angle subtended by the same arc at the circumference?
It is twice the angle subtended at the circumference.
State the Alternate Segment Theorem.
The angle between the tangent and the chord at the point of contact is equal to the angle in the alternate segment.
What is the Angle in a Semicircle Theorem?
A triangle inscribed in a semicircle is a right triangle, with the right angle opposite the diameter.
State the Congruent Chords Property.
Equal chords in a circle subtend equal angles at the center.
What can be said about angles in the same segment?
Angles in the same segment of a circle are equal.
If two tangents are drawn to a circle from an external point, what can be said about their lengths?
The two tangents drawn from an external point are equal in length.
What is the Angle Between Radius and Tangent Theorem?
The angle between the radius and tangent at the point of contact is 90 degrees.
Explain the concept of a Cyclic Quadrilateral.
A quadrilateral is cyclic if its vertices all lie on the circumference of a circle.
What is special about the opposite angles of a cyclic quadrilateral?
The opposite angles of a cyclic quadrilateral add up to 180 degrees.
State the Perpendicular from the Center Theorem.
A line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.
Describe the relationship between an arc and its chord.
The angle subtended at the center by an arc is larger than the angle subtended by the same arc at any other point on the circle.
What does the Power of a Point Theorem state?
For a point outside a circle, the product of the lengths of the two line segments from the point to the points of intersection of a line with the circle is constant.
What is a tangent?
A line that touches a circle at exactly one point.
How do you prove two lines are tangents if they meet a circle at a point?
Show that both angles formed with the radii are 90 degrees.
State the Equal Arcs Property.
If two arcs of a circle are equal, then the chords of those arcs are also equal.