help im having trouble

supersoccerqueen123

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May 18, 2005
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i have a really hard geometry question
its on how to prove that theorems are true for external angles. there is a circle and there is a secant and a tangent line connecting at one point outside the circle. the angle that they form is angle e. i have to prove that measurement of angle e is equal to 1/2 times (x-y) which is x is the arc farthest away from the angle e and y is the arc going towards the angle e. i have to prove that that theorem is true using a 2 column proof. can u help me? im stuck on where to start.
so far i have connected the end point of the tangent line on the circle to the other side of the circle which is where the secant is. i knew that those 2 angles are congruent because 2 tangents connecting are equal in 2 angles, i called them angles w. then the angle w on the side of the secant is supplemenatry to the angle necxt to it which i called angle z. please help!
 
What I did is call the center of the circle O and drew BO. The crossing point of BO and AC is Q. I'm calling <QCO x.
BQA is a right triangle.
<BQA = 90 - A :right triangle
<CQO = <BQA
CB = 180 - x - (90-A) :sum of angles
<QDO = x :isosolese triangle
<OQD = 90+A :Supplementary angles
BD = 180 - (90 + A) - x :sum of <s
Subtract BD from CB
 
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