Chapter 12

Chords, Secants, and Tangents

12-1 Circles in the coordinate plane

Objective: Write the equation of a circle.

12-2 Properties of Tangents

Objective: Apply properties of tangents.

(x + 9)2  +  y2  =  121radius =

center:

radius = √15

center:  (3, ­ 5)

Write an equation of the circle withthe given center passing through thegiven point.

A diameter of a circle has endpoints ( ­2, 5) and ( 4, 7).Write the equation of the circle.

Tangent to a circle: a line in the plane of the circle that intersects the circle in exactly one point.

Point of tangency: the point where a circle and a tangent intersect

Theorem 12-2

If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

The triangle below is circumscribed about the circle.

The circle is inscribed in the triangle.

Theorem 12-4

Two segments tangent to a circle from a point outside the circle are congruent.

If m<ABC = 43°, Find m<AOC.

HW # 112p. 590 # 27 *Quiz Friday!p. 596-98 # 1-6, 14-16