Question 1143643: A triangle ABC is inscribed in a circle with radius, R having its center at O.
If angle OBA is 48degrees .Determine the angle ACB .
--can you plss draw the fig. Thankyou
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source):
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The radius of the circle, R, has nothing to do with the problem....
You can draw the figure....
(1) draw the circle with center O
(2) draw radius OB
(3) place A on the circle so that angle OBA is 48 degrees (it's a sketch; it doesn't have to be exact....)
To see how to solve the problem, place a new point D on the circle so that BD is a diameter.
Since angle OBA is 48 degrees, the measure of arc AD is 96 degrees.
Since BD is a diameter, arc DAB is 180 degrees, so minor arc AB is 84 degrees.
So side AB of the inscribed triangle divides the circle into a minor arc AB of measure 84 degrees and a major arc ADB of measure 276 degrees.
There are then exactly two possible measures of angle ACB:
If C is anywhere on minor arc AB, then the arc cut off by angle ACB is 276 degrees, making angle ACB 138 degrees;
If C is anywhere on major arc ADB, then the arc cut off by angle ACB is 84 degrees, making angle ACB 42 degrees.
ANSWER: With the given conditions, angle ACB can have a measure of either 42 degrees or 138 degrees.
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