$R + G + B$

Geometry Level 2

$\triangle ABE$ and $\triangle DBC$ are both right angled triangles(with $\angle ABC$ as right angle), and circle with center in $O$ is inscribed to both of these triangles. What is the sum of $\color{#3D99F6}blue$ , $\color{#D61F06}red$ , and $\color{#20A900}green$ angle in degrees?

The answer is 90.

1 solution

Vittorio Bertoletti
Mar 16, 2018

If the sum $\color{#3D99F6}{\theta_{blue}} \color{#333333}{+} \color{#D61F06}{\theta_{red}} \color{#333333}{+} \color{#20A900}{\theta_{green}}$ must be constant we can consider the "limit case" where $A\equiv D$ and $C\equiv E$ : in this case $\color{#D61F06}{\theta_{red}}\color{#333333}{=0°}$ while $\color{#3D99F6}{\theta_{blue}} \color{#333333}{+} \color{#20A900}{\theta_{green} \color{#333333}{+ 90° = 180°}}$ so $\color{#3D99F6}{\theta_{blue}} \color{#333333}{+} \color{#D61F06}{\theta_{red}} \color{#333333}{+} \color{#20A900}{\theta_{green}} \color{#333333}{=90°}$ .

R + G + B R + G + B R + G + B

The answer is 90.

1 solution

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$R + G + B$