🔥 New! 2025 AMC 10 B

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Problem 5 Easy

In \triangle A B C, A B = 1 0, A C = 1 8, and \angle B = 1 3 0 ^ { \circ }. Let O be the center of the circle containing points A, B, and C. What is the degree measure of \angle CAO?

  • A.

    20

  • B.

    30

  • C.

    40

  • D.

    50

  • E.

    60

Answer:C
Solution

\angle ABC = 130^\circ \implies \angle AOC = 2 \times (180^\circ - \angle ABC) = 2 \times 50^\circ = 100^\circ

OA = OC \implies \angle OAC = \frac{1}{2} \times (180^\circ - \angle AOC) = \frac{1}{2} \times (180^\circ - 100^\circ) = 40^\circ

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