3RD Quarter Review: Theorems Flashcards
This is where the measure of a central angle
of a circle is equal to the measure of its intercepted arc.
CA-IA Postulate
What is the Arc Addition Postulate?
The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs
A line on a plane of the circle that
intersects the circle at exactly one point.
Not a
Tangent
The point at which the circle and the tangent intersect is called the?
Point of Tangency
A line or a segment that is tangent to two
circles in the same plane
Common Tangent
What is the Common Internal Tangent?
Intersects the segment joining the centers of the two circles.
Do not intersect the segment joining the
centers of the two circles
Common External Tangent
- Circles that intersect at exactly one point.
Tangent Circles
Circles that are coplanar, share a common point of
tangency, and with centers that lie on the same side of their common tangent
Internally Tangent Circles
Circles that are coplanar, share a common point of
tangency, and with centers that lie on the opposite sides of their common tangent.
Externally Tangent Circles
A polygon is [blank] about circle if all
of its sides are tangent to a circle
Circumscribed
A polygon is [Blank] in a circle if all of its vertices are on the circle.
Inscribed Polygon
What is the Tangent Line Theorem?
If a line is tangent to a circle, then it is perpendicular to the
radius drawn to the point of tangency.
In a plane, if a line is perpendicular to a radius of a circle,
then the line is a tangent to the circle.
The Converse Tangent Line Theorem
The Tangent Segments Theorem
1.The two tangent segments are congruent, and
2.The angles between the tangent segments and the line joining the external point to the center of the circle are congruent.
The line segments from the point of intersection to each of the points of tangency are congruent.
Intersecting Tangents Theorem
The product of the length of a secant segment and the length of its external segment is equal to the product of the length of the other segment and the length of its external segment.
Intersecting Secants Theorem
The square of the length of the tangent segment is
equal to the product of the length of the secant segment and the length if its external segment.
Intersecting Secant and Tangent
The Inscribed Angle Theorem
The measure of an inscribed angle of a circle is equal to
half the measure of its intercepted arc.
An angle inscribed in a semicircle is a right angle.
The Semicircle Theorem
Inscribed Angles in the Same Arc Theorem
If two inscribed angles intercept the same arc, then they are congruent.
Opposite angles of an inscribed
quadrilateral are supplementary.
Inscribed Quadrilateral Theorem
