Question

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.

Answer 1

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

`\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`