Math CentralQuandaries & Queries


Question from R2D2, a student:

A triangle is inscribed in a circle of radius 10. If two angles are 70 degrees and 50 degrees find the length of the side opposite the third angle?


Clearly, this problem has been designed to be very easy for those who know some geometry, and much harder for those who fail to use the familiar theorems. Draw a picture to scale. What’s the measure of the third angle? What do you know about the length of a chord that subtends that angle. (Hint: all inscribed angles on the same side of this chord have the same measure — including the one whose vertex lies on its perpendicular bisector.)



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