MathDB
2019 Geometry # 6

Source:

September 10, 2023
geometry2019

Problem Statement

Consider a triangle △ACE\vartriangle ACE with ∠ACE=45o\angle ACE = 45^o and ∠CEA=75o\angle CEA = 75^o. Define points Q,RQ, R, and PP such that AQAQ, CRCR, and EPEP are the altitudes of △ACE\vartriangle ACE. Let HH be the intersection of AQAQ, CRCR, and EPEP. Next define points B,DB, D, and FF as follows. Extend EPEP to point BB such that BP=HPBP = HP, extend AQAQ to point DD such that DQ=HQDQ = HQ, and extend CRCR to point FF such that FR=HRF R = HR. Finally, lengths CH=2CH = 2, AH=2AH =\sqrt2, and EH=3−1EH =\sqrt3 - 1. Compute the area of hexagon ABCDEFABCDEF.
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