   SEARCH HOME Math Central Quandaries & Queries  Question from Greg: A trapezoid is inscribed within a circle. The two interior angles who share the longest side are 70 and 80. The arc whose chord is the longest side has a length of 120. Find the other two interior angles of the trapezoid, and the other three arc lengths. Greg,

Something is wrong here -- a trapezoid inscribed in a circle MUST be isosceles. Consequently, the two interior angles that share the longest side must be equal. For example, if the base angles are both 80 degrees, the two top angles of your trapezoid would both be 100 degrees. Another problem, it sounds as if you are giving the measure of the arc in degrees -- that is NOT the length, but it is the angle at the center of the circle that is subtended by the arc. If that is the case, then the theorem you need to finish your problem is "the angle between two secants that intersect outside the circle equals the half difference in the measures of two arcs that the angle cuts from the circle." See

Chris     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.