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Honors Geometry_9.3_March 2 Warmup 1) Solve for x. C is center P is point of tangency 6 C x 8 2) Solve for x and y. P Both the Blue line and purple line 8 Revisit THEOREM 9.1 if necessary are tangent to the circle x 18 y 18 60˚ 9-3 Arcs and Central Angles I can ... explain how to find the measure of a given arc or a given central angle. I can... solve real world problems involving central angles and arcs of circles. [G.CO.1, G.C.2] 1 Honors Geometry_9.3_March 2 CENTRAL ANGLE - an angle with its vertex at the center of the circle & whose two sides are radii. ARC - portion of the edge of the circle defined by two endpoints. MINOR ARC - arc that is in the interior of the central ∠. - measure will be less than 180˚. - Use 2 letters to name. MAJOR ARC - arc with a measure greater than 180˚ - Use 3 letters to name. SEMICIRCLE - arc with endpoints on the diameter. - measure equals 180˚. - Use 3 letters to name. MEASURING ARCS Measures of arcs are related to corresponding central angles. measure of a minor arc - the measure of its central angle measure of a major arc - 360˚ minus the measure of the minor arc. measure of a semicircle - 180˚ 2 Honors Geometry_9.3_March 2 Two arcs of the same circle are adjacent if they intersect at exactly 1 point. You can add the measures of adjacent angles using... Arc Addition Postulate: The measure of the arc formed by 2 adjacent arcs is the sum of the measures of the 2 arcs. Two arcs of the same circle or of congruent circles are congruent arcs if they have the same measure. Theorem 9.3 In the same circle or in congruent circles, 2 minor arcs are congruent if and only if their central angles are congruent. 50o 50o 3 Honors Geometry_9.3_March 2 Name the following: (O is the center) a) two minor arcs b) two major arcs c) two semicircles C , , etc. R O d) an acute central angle S A e) two congruent arcs Give the measure of each angle or arc. YT is a diameter. a) mWX = _______ b) mXY = _______ Y X 30 o c) m∠WOT = _______ d) mYZT = _______ e) m∠YOT = _______ O Z W 50 o T f) mXYT = _______ 4 Honors Geometry_9.3_March 2 Find: D E 4 -1 x 2 4x 2x 3 3x x+1 0 A) mAB = _____ C B) mEDB = ______ B A [first find 'x'] Assignment P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16 5 Honors Geometry_9.3_March 2 9.3 Assignment: P. 341 CE 1-13; WE 2-6 even; 7, 8, 10, 11, 16 150˚ 6 Honors Geometry_9.3_March 2 7 Honors Geometry_9.3_March 2 Answers 2)80 4) 50 6) 55 7) 30 8) 4,8 10) 60 30 11) 16) 35 70, 70 2n 3k 56 50 2x 70 50 2x 35 28 #10 & 11 HINT: Make isosceles triangles 34 44 100 88 104 p + q 50 44 50 1/2(p+q) 8