1. Additional Topics in Math Lessons 3-4
Basic Circle Terms
Angles in a Circle
Area of Sectors
Angles Formed by Chords, Tangents, and Secants
Lengths of Chords, Tangents and Secants
Intersection of Circles
Derivation and Application of Trigonometric Ratios
The Pythagorean Theorem

2. Basic Circle Terms
Circle: Set of points a given distance from a set point
The set point is called the Center
The given distance is called the Radius
Chord: Line segment joining two point on the circle
Diameter: Chord that passes through the center
Arc: Section on the circle, past of the curve
chord
radius
diameter
arc

3. Angles in a Circle Full circle = 360̊ Semicircle = 180̊
Central Angle: Vertex is at the center
The angle measure equals the arc measure
Inscribed Angle: Vertex is on the circle
The angle measure equals half the arc measure
70°
70°
120°
60°

4. Area of Sectors Area of a Circle: πr2
Sector of a circle: A piece of a circle
Area of a sector = sector angle/360° ∙ πr2

5. Angles formed by Chords, Tangents, & Secants
Tangent: Line segment that touches the circle exactly once, at an angle perpendicular to a radius
Tangents drawn to circle from exterior points are congruent
Secant: A line that intersects the circle twice
An angle formed with a chord and a tangent is equal to half the intercepted arc
An angle formed by two secants equals half the difference of the intercepted arcs
An angle formed by two chords crossing equals half the sum of the intercepted arcs.

6. Lengths of Chords, Tangents, & Secants
A radius cuts a chord in half
All radii are equal
Two chords that intersect have equal products
Secants have equal products if you multiple the whole secant by the length of the external piece 2 4 4 3 5 4 2 6 3 3 5 4 6

7. Intersection of Circles
Intersecting circles have a common chord
The common chord is perpendicular to the line connecting the centers

8. Derivation and Application of Trigonometric Ratios
You must remember soh-cah-toa
Sin Ɵ = opposite/hypotenuse
Cos Ɵ = adjacent/hypotenuse
Tan Ɵ = opposite/adjacent
hypotenuse
opposite Ɵ
adjacent

9. The Pythagorean Theorem
You can only use the Pythagorean Theorem on Right Triangles
a2 + b2 = c2
Memorizing some Pythagorean Triples will be helpful
3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17
6, 8, 10
9, 12, 15
hypotenuse
leg
leg