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Omni-MATH / Triangle ABC satisfies ∠B>∠C. Let M be the midpoint of BC, and let the perpendicular bisector of BC meet the circumcircle of △ABC at a point D such that points A,D,C, and B appear …

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problem

Triangle ABCA B C satisfies ∠B>∠C\angle B>\angle C. Let MM be the midpoint of BCB C, and let the perpendicular bisector of BCB C meet the circumcircle of △ABC\triangle A B C at a point DD such that points A,D,CA, D, C, and BB appear on the circle in that order. Given that ∠ADM=68∘\angle A D M=68^{\circ} and ∠DAC=64∘\angle D A C=64^{\circ}, find ∠B\angle B.
Plain-text mathematical notation (without MathML)
Triangle ABC satisfies ∠B>∠C. Let M be the midpoint of BC, and let the perpendicular bisector of BC meet the circumcircle of △ABC at a point D such that points A,D,C, and B appear on the circle in that order. Given that ∠ADM=68^(∘) and ∠DAC=64^(∘), find ∠B.
Original LaTeX notation
Triangle $A B C$ satisfies $\angle B>\angle C$. Let $M$ be the midpoint of $B C$, and let the perpendicular bisector of $B C$ meet the circumcircle of $\triangle A B C$ at a point $D$ such that points $A, D, C$, and $B$ appear on the circle in that order. Given that $\angle A D M=68^{\circ}$ and $\angle D A C=64^{\circ}$, find $\angle B$.

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Source and history

task_id
e9e3a18b-841c-5bef-a38e-c409cb3ca4f9
task_key
test--e9e3a18b-841c-5bef-a38e-c409cb3ca4f9
task_revision_id
1
config / split
/ test

Official source

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