1. Essential Question: How do we use the theorems of circles?
Review for Unit Test
Saturday, June 02, 2018
Essential Question:
How do we use the theorems of circles?
M2 Unit 3: Day 13

2. . Arcs and Chords arc of the chord   chord
-Two minor arcs are  if and only if their corresponding chords are 
- Inscribed polygons has each vertex on the circle
- If the diameter of a circle is perpendicular to a chord, it bisects the cord & the arc
-Two chords are  iff they are equidistant from the center. 11 .

3. Inscribed Angles red & blue ∠‘s are 
Intercepted arc
An inscribed ∠ has its vertex on the circle
Inscribed polygons have all vertices on the circle
Opposite ∠ ‘s of inscribed quadrilaterals are supplementary
The measure of inscribed ∠’s = ½ intercepted arc
If an inscribed ∠ intercepts a semicircle, the m∠ = 90°
If 2 inscribed ∠ ‘s intercept the same arc, the ∠‘s are 
red & blue ∠‘s are 

4. Tangents •
Tangent lines intersect the circle at 1 point—the ‘point of tangency’
A line is tangent to the circle iff it is perpendicular the the radius drawn at that particular point
If a point is outside the circle & 2 tangent segments are drawn from it, the 2 segments are congruent. . •
Tangents can be internal or external  

5. Secants, Tangents & Angle MeasuresI
A secant line intersects the circle in 2 points
Intersecting at point of tangency A B C D
1 secant & 1 tangent

6. Secants, Tangents & Angle MeasuresB C D 1 2
Intersection in interior of circle
2 secants: forms 2 pair of vertical angles
Vertical ∠ are 

7. Secants, Tangents & Angle Measures
Intersection at exterior point
Case 1 2 secants C B P A D C D
Case 2 1 secant & 1 tangent P A B
Case 3 2 tangents B P Q A

8. Special Segments in a Circleb c d
If two chords intersect inside (or outside) of a circle, the products of their segments are equalab = cd x a b c
2 secants & exterior point::
a(a + x) = b(b + c)
1 tan and 1 sec & exterior point
a2 = x(x + b)
= x2 + bx a x b

18. Homework:
Finish Unit 3 Study Guide
(Unit 3 Test is tomorrow)