MathDB
Trapezoid + Bisectors

Source: AMC 12 2008B Problem 25

February 28, 2008
geometrytrapezoidrectangletrigonometrycircumcirclesymmetryratio

Problem Statement

Let ABCD ABCD be a trapezoid with AB∥CD AB\parallel{}CD, AB\equal{}11, BC\equal{}5, CD\equal{}19, and DA\equal{}7. Bisectors of ∠A \angle A and ∠D \angle D meet at P P, and bisectors of ∠B \angle B and ∠C \angle C meet at Q Q. What is the area of hexagon ABQCDP ABQCDP? <spanclass=′latex−bold′>(A)</span> 283<spanclass=′latex−bold′>(B)</span> 303<spanclass=′latex−bold′>(C)</span> 323<spanclass=′latex−bold′>(D)</span> 353<spanclass=′latex−bold′>(E)</span> 363 <span class='latex-bold'>(A)</span>\ 28\sqrt{3}\qquad <span class='latex-bold'>(B)</span>\ 30\sqrt{3}\qquad <span class='latex-bold'>(C)</span>\ 32\sqrt{3}\qquad <span class='latex-bold'>(D)</span>\ 35\sqrt{3}\qquad <span class='latex-bold'>(E)</span>\ 36\sqrt{3}
Back to ProblemsView on AoPS