ANALYTIC ANALYSIS OF LINES and CIRCLES
CHAPTER 1: ANALYTIC ANALYSIS OF LINES
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1. THE COORDINATE PLANE
A. ANALYTIC ANALYSIS OF POINTS
B. ANALYTIC ANALYSIS OF TRIANGLES
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2. ANALYTIC ANALYSIS OF LINES
A. TRIGONOMETRIC RATIOS OF ANGLES
B. SLOPE OF A LINE
C. EQUATION OF A LINE
D. FINDING THE SLOPE OF A LINE WITH A GIVEN EQUATION
E. RELATIVE POSITION OF TWO LINES
F. FIRST DEGREE INEQUALITIES IN TWO UNKNOWNS
G. BUNCH OF LINES (OPTIONAL)
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3. FURTHER APPLICATIONS
A. ANGLES BETWEEN TWO LINES
B. DISTANCE FROM A POINT TO A LINE
C. DISTANCE BETWEEN TWO PARALLEL LINES
D. EQUATIONS OF ANGLE BISECTORS
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4. SYMMETRY
A. SYMMETRY OF A POINT
B. SYMMETRY OF A LINE (OPTIONAL)
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CHAPTER 2: ANALYTIC ANALYSIS OF CIRCLES
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1. EQUATION OF A CIRCLE
A. STANDARD EQUATION OF A CIRCLE
B. GENERAL EQUATION OF A CIRCLE
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2. POSITIONS OF LINES AND CIRCLES
A. RELATIVE POSITION OF A LINE AND A CIRCLE
B. EQUATIONS OF TANGENT AND NORMAL LINES
C. RELATIVE POSITION OF TWO CIRCLES
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3. POWER OF A POINT, RADICAL AXIS, AND RADICAL CENTER
A. POWER OF A POINT
B. RADICAL AXIS OF TWO CIRCLES
C. RADICAL CENTER OF THREE CIRCLES
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4. FURTHER APPLICATIONS ON CIRCLES (OPTIONAL)
A. PARAMETRIC EQUATIONS OF A CIRCLE
B. EQUATION OF A SEMI-CIRCLE
C. INEQUALITIES INVOLVING CIRCLES
D. FAMILY OF CIRCLES