MathDB
2014 Guts #19: Bisectors in a Trapezoid

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April 21, 2014
geometrytrapezoid

Problem Statement

Let ABCDABCD be a trapezoid with AB∥CDAB\parallel CD. The bisectors of ∠CDA\angle CDA and ∠DAB\angle DAB meet at EE, the bisectors of ∠ABC\angle ABC and ∠BCD\angle BCD meet at FF, the bisectors of ∠BCD\angle BCD and ∠CDA\angle CDA meet at GG, and the bisectors of ∠DAB\angle DAB and ∠ABC\angle ABC meet at HH. Quadrilaterals EABFEABF and EDCFEDCF have areas 2424 and 3636, respectively, and triangle ABHABH has area 2525. Find the area of triangle CDGCDG.
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