Is a cyclic quadrilateral?
Since is perpendicular to ,
is a right-angled triangle at . First, use the
fact that the sum of the measures of the interior angles of a
triangle is to find the measure of .
The measure of is the same as the measure of , so the measure of is . If were a cyclic quadrilateral, then would be an inscribed angle subtended by . Also, would be an inscribed angle subtended by . Since the measures of inscribed angles subtended by the same arc are equal, the measure of would be equal to the measure of . However, since measures , and measures , this is not the case. Thus, is not a cyclic quadrilateral.