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This review covers the theorems of circles, including inscribed polygons, chords, arcs, tangent lines, secants, and angle measures. Prepare for the upcoming unit test by studying these concepts and completing the assigned homework.
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Review for Unit Test Thursday, November 7, 2019 Essential Question: How do we use the theorems of circles? M2 Unit 3: Day 13
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 .
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
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
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
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
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
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
Homework: Finish Unit 3 Study Guide (Unit 3 Test is tomorrow)