Review for Unit Test

1. Review for Unit Test Thursday, November 7, 2019 Essential Question: How do we use the theorems of circles? M2 Unit 3: Day 13

2. Arcs and Chords -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. arc of the chord   chord 11 11 .

3. An inscribed ∠ has its vertexon 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  Inscribed Angles  Inscribed ∠ Intercepted arc red & blue ∠‘s are

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

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

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

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