kude111

Chapter 9.1 [|some definitions] Circle- The set of points in a plane that are equidistent from a givin point known as the center of the circle. Radius- Asegment that connects the center of a circle with a point of the circle. Chord- Segment whose endpoints lie on a circle. Diameter- Chorde that passes through the center of a circle. Arc- Unbroken part of a circle. Endpoints- Points at the end of a segment or starting point. Semi Circle- The arc of a circle whose endpoints are the endpoints of diameter. Minor Arc- An arc of a circle that is shorter than a semi circle of that circle. Major Arc- An arc of a circle that is longer than a semicircle of that circle. Central Angle- Angle formed by 2 rays. Intercepted Arc- An arc whose endpoints lie on the sides of an inscribed angle. Degree measure of arcs- The measure of a minor arc is the measure of its central angle.

Chapter 9.2 Secant- A line that intersects a circle at two points. Tangent- In a right triangle the ratio of the length of the sides opposite an acute angle to the length of the sides adjacent to it. Point of tangency- The point of intersection of a circle or sphere with a tengent line or plain. [|Some examples]

Chapter 9.3 Inscribed angle-is a angle whose vertex lives on a crcle and whose side are chords of the circle. Inscribed Angle Theorem-the measure of an angle inscribed in a circle is egual to half the measure of the intercepted. Right-Angle Corollary-if an inscribed angle intercepts a semicircle then the angle is a right angle. Arc-Intercept Corollary-if two inscribed angles intercept the same arc then they have the same measure Chapter 9.4 Case 1- vertex is one of the circle Case 2- is inside the circle
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Case 3- is outside the circle

Theorem- If a tangent and secant intersept on a circle at the point of tangency then the measure of the angle formad is half the measure of its intercepted act. Chapter 9.5