Chapter 12 Circles Vocab

Circle – the set of all points in a plane a given distance away from a center point. A A circle is named by its center point. For example: Circle A or A. Radius – the “given distance away from the center point” of a circle; a segment that joins the center to a point on the circle. Radius (r)Plural: Radii

Sphere – the set of all points a given distance away from a center point.

Chord – a segment whose endpoints lie on on the circle. Example: DC AB C D Diameter – a chord that passes through the center of the circle.Example: AB A diameter is twice the length of a radius.

Secant – a line that contains a chord. Example: AB A B **Note: A chord and a secant can be named using the same letters. The notation tells you whether it is a secant or a chord. A secant is a line; a chord is a segment.** Secant: AB Chord: AB

Tangent – a line that intersects a circle at exactly one point. Not a tangent! A B The point at which the circle and the tangent intersect is called the point of tangency. Example: A Example: AB

Section Tangents

Theorem 12-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. If AB is tangent to Circle Q at point C, then QC  AB. ABC Q Q is the center of the circle. C is a point of tangency.

Example: Given Circle Q with a radius length of 7. D is a point of tangency. DF = 24, find the length of QF. FD Q = QF 2 QF = 25 Extension: Find GF. G QG = 7QF = 25 GF = 18 NOTE: G is NOT necessarily the midpoint of QF!!

Theorem 12-2: If a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. This is the converse of Theorem 12-1.

Theorem 12-3: IF two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.

Common Tangent – a line that is tangent to two coplanar circles. Common Internal Tangent Intersects the segment joining the centers.

Common External Tangent Does not intersect the segment joining the centers.

Tangent Circles – coplanar circles that are tangent to the same line at the same point. Internally Tangent Circles Externally Tangent Circles

Congruent Circles – circles with congruent radii. 5cm Concentric Circles – circles with the same center point.

When each side of a polygon is tangent to a circle, the circle is said to be inscribed in the polygon. This circle is inscribed inside of the pentagon.

When each vertex of a polygon is on the circle, the circle is said to be circumscribed around the polygon. This circle is circumscribed around the pentagon