Section 9 1 Circles Vocab Circle the set

Section 9 -1 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 (r) Plural: Radii Radius – the “given distance away from the center point” of a circle; a segment that joins the center to a point on the circle.

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 A B 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. B A Example: AB **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. B A Example: AB Not a tangent! The point at which the circle and the tangent intersect is called the point of tangency. Example: A

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

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

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.

Section 9 -2 Tangents

Theorem 9 -1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Q is the center of the circle. C is a point of tangency. Q A C B If AB is tangent to Circle Q at point C, then QC ^ AB.

Example: Given Circle Q with a radius length of 7. D is a point of tangency. DF = 24, find the length of QF. 72 + 242 = QF 2 QF = 25 Q 7 D G 24 F Extension: Find GF. QF = 25 QG = 7 NOTE: G is NOT necessarily the midpoint of QF!! GF = 18

Theorem 9 -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 9 -1.

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

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.