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Omni-MATH / Let ABC be a triangle and ω be its circumcircle. The point M is the midpoint of arc BC not containing A on ω and D is chosen so that DM is tangent to ω and is on the same side of …

Problem

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problem

Let ABCA B C be a triangle and ω\omega be its circumcircle. The point MM is the midpoint of arc BCB C not containing AA on ω\omega and DD is chosen so that DMD M is tangent to ω\omega and is on the same side of AMA M as CC. It is given that AM=ACA M=A C and ∠DMC=38∘\angle D M C=38^{\circ}. Find the measure of angle ∠ACB\angle A C B.
Plain-text mathematical notation (without MathML)
Let ABC be a triangle and ω be its circumcircle. The point M is the midpoint of arc BC not containing A on ω and D is chosen so that DM is tangent to ω and is on the same side of AM as C. It is given that AM=AC and ∠DMC=38^(∘). Find the measure of angle ∠ACB.
Original LaTeX notation
Let $A B C$ be a triangle and $\omega$ be its circumcircle. The point $M$ is the midpoint of arc $B C$ not containing $A$ on $\omega$ and $D$ is chosen so that $D M$ is tangent to $\omega$ and is on the same side of $A M$ as $C$. It is given that $A M=A C$ and $\angle D M C=38^{\circ}$. Find the measure of angle $\angle A C B$.

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Source and history

task_id
f8c5f2e7-afe5-56de-95f8-eb011be2a46d
task_key
test--f8c5f2e7-afe5-56de-95f8-eb011be2a46d
task_revision_id
1
config / split
/ test

Official source

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