Question 889442: I am having trouble with this problem. They want me to find the measure of angle 0 when the measure of the major arc off the circle is 198 degrees. Please help!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! I need more information.
where is angle O?
is it in the middle of the circles, somewhere else inside the circle, on the surface of the circle? outside the circle?.
all of these will give you a different answer.
here's a reference that might help you.
it covers all the possible scenarios you should encounter.
let me know if it helped and, if not, give me more details about the question so i can understand what exactly you are looking for.
http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm
thank you for replying.
the angle, if i understood you correctly, is the vertex of 2 tangent lines that creates a major arc on the outside of the intersection points.
the formula involved in solving your problem is:
angle = 1/2 * (major arc - minor arc).
in your problem, the major arc is 198 degrees.
that makes the minor arc equal to 360 - 198 = 162 degrees.
the formula becomes:
angle = 1/2 * (198 - 162) = 1/2 * 36 = 18 degrees.
that is the measure of your angle that is the intersection of the two tangent lines.
that same value can also be found by forming an isosceles triangle from the points of tangency to the vertex of the tangent lines to the center of the circle.
since the minor arc is 162 degrees, each of the right triangles formed has an angle of 81 degrees.
this makes the other angle of each of those right triangles equal to 9 degrees which equals 18 degrees when you add them both together.
the following picture shows you what i mean.
since the central angle is the same measure as its subtending arc, an arc of 198 degrees has a central angle of 198 degrees and an arc of 162 degrees has a central angles of 162 degrees, as shon in the picture.
check out the reference.
it's a good one.
your particular situation is in number 5.
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