Problem 153

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Problem 153: (2025 AMC 10b, 5)

In $\triangle ABC$, $AB=10$, $AC=18$, and $\angle B=130^\circ.$ Let $O$ be the center of the circle containing $A$, $B$, and $C.$ What is the degree measure of $\angle CAO$? $\textbf{(A)}~20 \qquad$ $ \textbf{(B)}~30 \qquad$ $ \textbf{(C)}~40 \qquad$ $ \textbf{(D)}~50 \qquad$ $ \textbf{(E)}~60$

Solution

Exercise 153: Solution

In $\triangle ABC$, $\angle B=75^\circ$ and $\angle C=45^\circ$. Let $O$ be the center of the circle through $A$, $B$, and $C$, and let $H$ be the foot of the altitude from $A$ to $\overline{BC}$. What is the degree measure of $\angle OAH$?

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