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In acute triangle $$ABC$$,$$\angle A = 68^\circ.$$ Let $$O$$ be the circumcenter of triangle $$ABC$$. Find$$\angle OBC$$, in degrees.

Feb 18, 2019

#1
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In acute triangle $$ABC,\ \angle A = 68^\circ$$.

Let be the circumcenter of triangle $$ABC$$.
Find, $$\angle OBC$$ in degrees.

$$\text{Let \angle OBC = {\color{red}x} }$$

$$\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}$$

$$\text{\angle OBC in degrees is 22^{\circ}}$$

Feb 19, 2019

#1
+21848
+4

In acute triangle $$ABC,\ \angle A = 68^\circ$$.

Let be the circumcenter of triangle $$ABC$$.
Find, $$\angle OBC$$ in degrees.

$$\text{Let \angle OBC = {\color{red}x} }$$

$$\begin{array}{|rcll|} \hline 2{\color{red}x} + 2{\color{blue}y} + 2{\color{green}z} &=& 180^{\circ} \quad | \quad : 2 \\ {\color{red}x} + {\color{blue}y} + {\color{green}z} &=& 90^{\circ} \quad | \quad {\color{blue}y} + {\color{green}z} = \angle A \\ {\color{red}x} + A &=& 90^{\circ} \\ {\color{red}x} &=& 90^{\circ} - A \quad | \quad A = 68^{\circ} \\ {\color{red}x} &=& 90^{\circ} - 68^{\circ} \\ {\color{red}x} &=& 22^{\circ} \\ \hline \end{array}$$

$$\text{\angle OBC in degrees is 22^{\circ}}$$

heureka Feb 19, 2019