moci308

**9.1**
__Chord--__ segment whose endpoints line on a circle __Diameter--__ A chord that contains the center of a circle __ Arc and diameter

Arc--__ An unbroken part of a circle __Endpoints--__ Any 2 distinct points on a circle divided the circle into 1 acts. __Semi-circle --__ An arc whose endpoints are endpoints of a diameter named by its endpoints and another point that lies on the arc. __Minor arc--__ og a circle is an arc that is shorter than a semi circle of that cicle named by its points __Major arc--__ of a circle is an arc that is longer than a cemi circle of that circle named by its endpoints and another point that lies on the arc __Central angle---__ a circle is an angle in the plane of a circle whose vertex is the center of the circle. Intercepted arc an arc whose endpoints lie on the sides of the angle and whose other points lie in the interior of the angle. __Degree measure of arcs--__ the measure of its central angle. The degree measuremetns of a majow arc is 360 degree minus the degree measure of its minoe arc. The degree measure a semi circle is 180 degree example

**9.2**
Objectives: 1. define tangents and secants of circles 2. Understand the relationshop between tagents and certain radi of circles 3. Understnd the geometry of a radius perpendicular to a chord of a circle

Words to know __Secant --__ To a circle is a line that intersects the circle at 2 points to a cut __Tangent --__ a line in the plane of the circle that intersects the circle at exactly 1point __Point of tangency__ -- doesnt touch the plane of the circle __Tangent Therom__ -- If a line is tangent to acircle then the lnine is perpendicular to a radius pf a circle drawn to the point of tagency __Radius and Chord Therom__ -- A radius that is perpendicular to a chord of a circle BISECTS the chord.

9.3
__Indescribed angle__ -- An angle whose vertex lies on a circle and whose sides are chords of the circle __Indescriced angle therom__ -- the therom of an angle inscribing in a circle is equal to half the measurement of the intercepted arc __Right-Angle Corollary__ -- If an inscribed angle intercepts a semi circle then the angle is a right angle __Arc intercept Colloary__ -- If two andgle intercepts the same arc then they have the same measure

9.4


Thereom If a tangent and a secant intersect on a circle at the point of tangency, then the measure of the angle forned is HALF the measure of its intercepted arc Example: THEROM 9.4.2 The measure of an Angle formed by 2 secants or chord that intersects in the interior of a circle is half the sum of the measure of the arc intercepted by its anfle and it's vertical angle.

THEROM 9.4.3 He measure of an angle formed by 2 secants that intercepted in the ecterior of a Circle is half the diffrence of the measure of the intercepted arc.

**9.5 Segments**
T =tangent O=putside of the circle segment W= whole Pt= Part Tagent segment -- are equal Seacant segment -- WxO= WxO Chord -- W-O= texp.2

9.6 Circles on Coordinate planes
x exp2 + y exp.2 =r exp.2
 * Circle equation with center at (0,0)**

Example

Formula x exp2 + y exp.2 =r exp.2 r=5

x exp2 + y exp.2 = 5exp.2 x exp2 + y exp.2 =

Equation of circle with center not at origin but at (h,k)
(x-h)exp.2 + (y-k) exp.2 = r exp.2 Center= (h,k) Radius= r

Example 2

Equation (x-h)exp.2 + (y-k) exp.2 = r exp.2 Center (5,4) Radius 3 (x-5)exp.2 + (y-4) exp.2 = 3 exp.2