9.12. Circles in the Coordinate Plane http://www.ck12.org
e. Now that we have the two perpendicular bisectors of the chord we can find their intersection. Solve the
system of linear equations to find the center of the circle.
f. Find the radius of the circle by finding the distance from the center (point found in parte) to any of the
three given points on the circle.
g. Now, use the center and radius to write the equation of the circle.Find the equations of the circles which contain the three points.
15.A(− 2 , 5 ),B( 5 , 6 )andC( 6 ,− 1 )
16.A(− 11 ,− 14 ),B( 5 , 16 )andC( 12 , 9 )Summary
This chapter begins with vocabulary associated with the parts of circles. It then branches into theorems about tangent
lines; properties of arcs and central angles; and theorems about chords and how to apply them. Inscribed angles and
inscribed quadrilaterals and their properties are explored. Angles on, inside, and outside a circle are presented
in detail and the subsequent relationships are used in problem solving. Relationships among chords, secants, and
tangents are discovered and applied. The chapter ends with the connection between algebra and geometry as the
equations of circles are discussed.
Chapter Keywords
- Circle
- Center
- Radius
- Chord
- Diameter
- Secant
- Tangent
- Point of Tangency
- Congruent Circles
- Concentric Circles
- Tangent to a Circle Theorem
- Central Angle
- Arc
- Semicircle
- Minor Arc
- Major Arc
- Congruent Arcs
- Arc Addition Postulate
- Inscribed Angle
- Intercepted Arc
- Inscribed Angle Theorem
- Inscribed Polygon
- Standard Equation of a Circle