escobarmaya2007 escobarmaya2007

26-04-2022
Mathematics

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In the accompanying diagram, AB is a diameter of circle O, FECA and
FBG are secants, AD, DE, EB = 1:3:2 and BG = 40°. Find the measures of AD,
DE, EB, and AG.

In the accompanying diagram AB is a diameter of circle O FECA and FBG are secants AD DE EB 132 and BG 40 Find the measures of AD DE EB and AG class=

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jdoe0001 jdoe0001

26-04-2022

Check the picture below.

so to split 180 in a 1 : 3 : 2 ratio, we'll simply divide 180 by (1 + 3 + 2) and distribute accordingly

[tex]\cfrac{180}{1+3+2}\implies 30\qquad \qquad \stackrel{1}{1(30)}~~:~~\stackrel{3}{3(30)}~~:~~\stackrel{2}{2(30)}\implies 30~:90~:60 \\\\[-0.35em] ~\dotfill\\\\ \widehat{AG}=180+40\implies \widehat{AG}=220[/tex]

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