chuab53

section 9-1 //In section 9-1 circles are used in construction, the degree and means u're of axes are explored, and there is the theorem of the intercepted arc.// ** __//circle//:__ pionts that come out from one piont at an equal distance(circle would be circle F) //__radius__//: a segment that extends from the center to the circle rim(DF is the radius/ or EF or CF) //__chord__//: a segment that doesn't cross the center point and touches two pionts on the circle(AB is a chord) __//diameter//:__ a sement that goes straight through the center and touches two pionts on the circle(EC is the diameter) //__arc__//: part of the circle that is unbrokenendpoints: two points that divide the arc(ABCis an arc) __//semi-circle//:__an arc whose endponts end on the diameter(EAC is a semi-cirlce) //__minor arc__:// arc less than the semi-circlemajor arc: arc more than the semi-circle(DEA is a minor arc) __//central angle//:__ anangle where the center of the circle is the vertex(measure angle DFE is a central angle) //__intercepted arc__//: an arc whose endpoints are the endpoints of the angle degree(DE is an intercepted arc) //__measure of arcs__//:simicircles' degree measure is 180, minor arc is the central angle, and major arc is 360 minus minor arcarc length: (r is radius, m is degree measure of arc, & L is the length of the arc) L=m/360degrees(2*pi*r) //chord and arcs theorem//: in a circle or circles the arcs of congruent chords are congruent __//converse of chords and arcs theorem//__: in cirles or congruent circles if the chords arcs are congruent the chords are congruent [|crop circles] Now that you know that th arc Edc is a semi circle so it equals 180 degrees, and you are told the minor arc DC is 100 degrees, how long is the minor arc ED? answer :80 degrees =section9-2=
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//In section 9-2 we learn about tange//nts //and secants of circles.We also learn about the relationship of tangent and radii,and the geometry of the chord perpendicular to the radius.// //__secant:__// line goes through the circle and touches two points //__tangent:__// a line that only touches the circle at one point //point of tangency:// the point where the line touches the circle //__tangent theorem__://if a line is tangent to a circle thte line is perpendicular to the radius of a circle //__converse of tangent theorem__:// If a line is perpendicular to a radious of a circle then the line is tangent to a circle //__radius and chord theorem:__//A radius that is perpendicular to the chord of a circle intersectsi the chord //__theorem__:// the perpendicular bisector of a chord passes through the center of the circle [|activity] If all angles that intercept at j are 90 degrees, the chor BE is 10 cm, and your using the radius chord theorem above, how long is BJ, BE? answer: they are both 5 cm =section 9-3= //In section 9-3 we define inscribed angle and intercepted arc, we also develop and use the inscribed angle and its corollaries.// //__Inscribed angle__:// an angle whose vertex is a pooint on a circleand the sides end on points on the circle //__Inscribed angle theorem__:// the measure of an angle incribed in a circle is equal to half the intercepted arc __//Right angle corollary://__ if and inscribed angle intercepts a semi-circle then the angle is a right angle //__Arc-intercept corollary__:// If two inscribed angles intercept the same arc then they ahve the same measure [|activity] refer to the picture in section 9-1 If the arc of DE is 90 degrees what is the measure of angleDFE? answer: 45 degrees =section 9-4= //In this section we define tangents of circles and secants that form angles.We alsodevelop and use theorems on measures of arcs//. [|] //__Case1__//:Vertex is on the circle //__Case2__//: Vertex is in the inside of the circle //__Case3__//: vertex is outside the circle //__theorem__://If a tangent and a secant intersect at the point of tangency, then the measureof the angle formed is the measure of the intercepted arc. //__theorem__//: The measure of an angle formed by two secants or chords that intersects in the interior of a circle is __the__of the measures of the arcs intercepted by the angle and its vertical angle. //__theorem__//: the measure of an angle formed by two secants that intersect the exterior of a circle is __the__ of the measures af an intersected arc. =section 9-5= //We define special cases of segments related to circles,we also use theorems to measure sements.// //__theorem__:// If two segments are tangent to a circle from the same external point, then the segmentsare equal. //__theorem__//: If two secants intersect outside a circle ,the product of the lenghts of one secant segment and the external segment equals the other secant segment. (whole secant *outside of secant= whole secan*outside of secant) //__theorem__//: If a secant and a tangent intersect outside a circle, then the product of the lenghts of the secant segment and its external segment equals, (whole of the secant* outside of the secant the tangent squared) //__theorem__:// if two chords intersect inside a circle, then the products of the lenghts of one segment of one chord equals the length f the other chord. In circle E, the lenghth of AC is 15in., and the length of BF is 9in., what is the length of FD. answer: 6in. =section 9-6= //We develop and use the equation of a circle and we learn to change equatons to make the center of a circle in a coordinate planes. // equations//:// If the circle is on the center to find the radius you use the equation:x squared plus y squared equals radius squared. If the circle is off center use the equation: (x-h)squared plus (y-k)squared equals radius squares [|take the quiz] //**warning**// you do have to scroll all the way don to the bottom to find it given x is 3 and y is 6 what is the radius answer:square root of 45
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 * fun sites:** [|tangents and secants]
 * example problems:** if arc CA is 40degrees andDJ is 10 digrees wht is the measure of angleDKJ? answer:10 degrees
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 * fun sites:** [|cool stuff on chords],tangents secants and arcs
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