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=__//9.3//__= Objectives-Define inscribed angle and intercepted arc Develop / use the Inscribed angle theorem and its corollaries

Definitions-
Inscribed angle-Andle whose vertex lie on the circle and whose sides are the chords of the circle---like this--- Intersecpted arc-the arc that is between the point on which the angles sides hit the circle---like this---



Theorems-
INscribed angle theorem-- The measure of an angle inscribed in a circle is equal to half the measure of the interceted arc--like this

Right-Angle Corollary-If an inscribed angle intersepts a semicircle then the angle is a right angle

like this

Arc-Intercept Corollary-If two inscribed angles intercept the same arc the they have the same measure---it would look like this--- Lets see how to use these in context say you are given this circle with this question lets do the one we can just get from the info given....Sense we know that central angles and there corresponding arcs are equal we know that arc AC is 60....now lets andd up all the arc amounts that we know and find the missing one by taking the total arcs we know and minusing them from 360 because there are a total of 360 degrees in a circle...so this is wat we have 125+115+60=300 .... and 360-300=60...so now we know all the arcs...arc AD=60...and sense we know the inscribed angle theorem we know that 30 is angle 4....also sense we know the radius and chords theorem we know that radius AP bisects CD making 2 right angles...so we know our picture will look like this.... Now we know angle 3 becasue it is the inscribed angle of arc AD and because of the inscribed angle theorem we know that the angle is halp the arc so angle 3 is 30 degrees and sense CD is bisecting triangle ACD we know that the corresponding angle to 3 is also 30 degrees so now we know that the measure of angle 1 because CP and AP are both radii and and both angle C and angle P are 60 and sense in a triangles angles 180 60 is the only answer to work!so this is what the circle will look like filled in\/



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