zini318

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__Objective__
Define tangents and secants or circles Understand the relationship between tangents and certain raddii of circle Understand the geometry of a radius perpendicular to a chord of a circl

__Definitions__
Circle- is a set of all points in a plane that are equidistant from a given oint in the plane known as the center of the circle ex. Radius- Segment from the center of the circle to any point on the circle ex . Chord- Also known as seacant is a segment that lies on the line in two places ex Diameter-A chord that contains the center of the circle ex

Arc-An unbroke part of the circle ex. Endpoints- A point at an end of a segment of the starting ray ex. Semi-Circle-The arc of a circle whose endpoints are the endpoints of the diameter ex. Minor arc-A arc less 180* Major Arc-A arc more than 180* Central angle- An angle formed b 2 rays originating for the center of a circle Intercepted Arc-An arc whose endpoints lie on the side of an inscribed angle Degree measure of arcs-The measure of a minor acr in te measure of its central angle. The degree measure of the major angle is 360* minus the degree of the central point Central angle- An angle formed by 2 rays with the originating for the center of the circle ex. Intercepted arc-An arc whose endpoints lie on the sides of an inscribed angle ex. Degree of measure of arcs-Te measure of a minor arc in the measure of its central angle, the degree meansure of a major arc is 360* minus the central angle example of a minor arc- say you have a cirlce with the central angle of 50* and arc measure would also be 50* because it is a minor arc...like this major arc- say you have a central angle that is 180* you would take 360 and minus it by 180 and get your answerre in this case it is 180* a semi-circle ex.

Example-

Arc Length
-If the radius(r) of any circle and M is the degree measure of an arc of the circle then then length L of the arc is given by the following: L=M/360*(2(pi)r) L=the length of the arc M=the measure of an arc of the circle 360*=the measure of any circle and 2(pi)r=the circumfrence of the circle Example- Find the length of this indicated arc.... say you have this cirlce you know that the radius is 25 because the segment that 25 is indicating goes from a point on the circle to the center point of the circle and you know that the measure arc of the circle is 35 degrees because the angle that is indicated is a central angle of the circle so you would fill these numbers into the generic equation we dont know length so we leave that empty L=35/360(2(pi)10) so the measure of the arc is 6.11 degrees

Chords and Arcs Theorom
In a circle or in two or more congruent circles the arcs of congruent chords are equal like this... Because the chords are congruent the arcs are congruent because of the chords arcs theorem To 9.2 Click here