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Thu 14 Jul, 2005 04:49 am
Segment AB is tangent to circle O at B, segment AB and segment ADC intersect at A and chord BC is congruent to chord CD. If the measure of arc BD = 60 and segment BC = 8, find the length of tangent segment AB.
This question is found in the chapter titled SOLVING TRIANGLES THAT INTERSECT CIRCLES AND THE LAW OF SINES.
I understand that BC and the measure of angle C = 1/2 times the measure of arc BD, which = 1/2 of 60 = 30.
Where do I go from there?
Since BC = CD, BCD is an isosceles triangle.
Therefore, angle CBD = angle CDB = 75.
Since arc BC = 150 and arc BD = 60, angle A = (150-60)/2 = 45.
Now you have two angles of triangle ABC, so angle ABC = 180-(30+45) = 105.
Since angle CBD = 75 and angle ABC = 105, angle ABD = 30 and angle ADB = 105.
Use the law of sines to determine BD.
Use it again to determine AB.
ok
I can take it from here. I will use your notes to review similar questions.
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