* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 10: Circles
Rational trigonometry wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Euler angles wikipedia , lookup
Problem of Apollonius wikipedia , lookup
Euclidean geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Chapter 10: Circles Objective: I will review and apply theorems related to circles 10.1 Circles and Circumference Name a circle by the letter at the center of the circle Diameter- segment that extends from one point on the circle to another point on the circle through the center point Radius- segment that extends from one point on the circle to the center point Chord- segment that extends from one point on the circle to another point on the circle Diameter=2 x radius (d=2r) Circumference: the distance around the circle C=2πr or C= πd 10.2 Angles, Arcs and Chords 10.2 Semi-circle: half the circle (180 degrees) Minor arc: less than 180 degrees Major arc: more than 180 degrees Name with two letters Name with three letters Minor arc = central angle Arc length: arc 2r 360 Find x and angle AZE 10.3 Arcs and Chords If two chords are congruent, then their arcs are also congruent In inscribed quadrilaterals, the opposite angles are supplementary If a radius or diameter is perpendicular to a chord, it bisects the chord and its arc If two chords are equidistant from the center of the circle, the chords are congruent A If FE=BC, then arc FE = arc BC B Quad. BCEF is an inscribed polygon – opposite angles are supplementary F angles B + E = 180 & angles F + C = 180 C E D Diameter AD is perpendicular to chord EC – so chord EC and arc EC are bisected Find the radius 10.4 Inscribed Angles Inscribed angle: an angle inside the circle with sides that are chords and a vertex on the edge of the circle Inscribed angle = ½ intercepted arc An inscribed right angle, always intercepts a semicircle If two or more inscribed angles intercept the same arc, they are congruent A. Find mX. Refer to the figure. Find the measure of angles 1, 2, 3 and 4. ALGEBRA Find mI. ALGEBRA Find mB. The insignia shown is a quadrilateral inscribed in a circle. Find mS and mT. 10.5 Tangents Tangent: a line that shares only one point with a circle and is perpendicular to the radius or diameter at that point. Point of tangency: the point that a tangent shares with a circle Two lines that are tangent to the same circle and meet at a point, are congruent from that point to the points of tangency 10.6 Secants, Tangents, and Angle Measures Secant and Tangent Two Secants: Interior angle = ½ (sum of intercepted arcs) Two Secants Interior angle = ½ intercepted arc Exterior angle = ½ (far arc – close arc) Two Tangents Exterior angle = ½ (far arc – close arc) A. Find x. B. Find x. C. Find x. A. Find mQPS. B. A. B. 10.7 Special Segments in a Circle Two Chords Two Secants seg1 x seg2 = seg1 x seg2 outer segment x whole secant = outer segment x whole secant Secant and Tangent outer segment x whole secant = tangent squared *Add the segments to get the whole secant A. Find x. B. Find x. Find x. LM is tangent to the circle. Find x. Round to the nearest tenth. Find x. Assume that segments that appear to be tangent are tangent. EXIT TICKET Find x. HOMEWORK P620 (1-15 odd, 17-20, 28-33, 41, 44, 47, 50)