Question 1143643
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The radius of the circle, R, has nothing to do with the problem....<br>
You can draw the figure....<br>
(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....)<br>
To see how to solve the problem, place a new point D on the circle so that BD is a diameter.<br>
Since angle OBA is 48 degrees, the measure of arc AD is 96 degrees.<br>
Since BD is a diameter, arc DAB is 180 degrees, so minor arc AB is 84 degrees.<br>
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.<br>
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.<br>
ANSWER: With the given conditions, angle ACB can have a measure of either 42 degrees or 138 degrees.