2021-12-22

Three chords with equal angles between them

This question was uploaded on 22/12/21 on social media accounts.

Solution:

Orange angles are inscribed at a common chord AB so they are similar,
Triangles ABC and AED have similar angles so both are similar triangles,
\[\Rightarrow \frac{AB}{AC} = \frac{AE}{AD}\]
Let EC = ? = x,
\[\Rightarrow \frac{14}{12+x} = \frac{12}{18}\]
\[\Rightarrow x = 9\]
Blue Line = ? = 9
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