I was not able to finish solving the exercise so I came to its solution but there is some part [yellow highlighted] is not possible to figure that out. How it is valid?
2026-04-03 01:48:29.1775180909
Show that $EGH + BGC + HGC = \frac12 ABCD.$
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We have $$EHC = EHB + CHB = \frac12 EDB + \frac 12 CDB = \frac12 EDC,$$ and $$EHC = \color{blue}{EGH + BGC + HGC} + \color{red}{EBG} = EGH + BGC + HGC + \color{red}{\frac 12 EAB}.$$ From the two equations,
$$ \color{blue}{EGH + BGC + HGC} = \frac12 EDC - \color{red}{\frac 12 EAB} =\frac12 ABCD.$$