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Omni-MATH / Let △ABC be a triangle inscribed in a unit circle with center O. Let I be the incenter of △ABC, and let D be the intersection of BC and the angle bisector of ∠BAC. Suppose that the…

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problem

Let △ABC\triangle A B C be a triangle inscribed in a unit circle with center OO. Let II be the incenter of △ABC\triangle A B C, and let DD be the intersection of BCB C and the angle bisector of ∠BAC\angle B A C. Suppose that the circumcircle of △ADO\triangle A D O intersects BCB C again at a point EE such that EE lies on IOI O. If cosA=1213\cos A=\frac{12}{13}, find the area of △ABC\triangle A B C.
Plain-text mathematical notation (without MathML)
Let △ABC be a triangle inscribed in a unit circle with center O. Let I be the incenter of △ABC, and let D be the intersection of BC and the angle bisector of ∠BAC. Suppose that the circumcircle of △ADO intersects BC again at a point E such that E lies on IO. If cosA=(12)/(13), find the area of △ABC.
Original LaTeX notation
Let $\triangle A B C$ be a triangle inscribed in a unit circle with center $O$. Let $I$ be the incenter of $\triangle A B C$, and let $D$ be the intersection of $B C$ and the angle bisector of $\angle B A C$. Suppose that the circumcircle of $\triangle A D O$ intersects $B C$ again at a point $E$ such that $E$ lies on $I O$. If $\cos A=\frac{12}{13}$, find the area of $\triangle A B C$.

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Source and history

task_id
713d7efc-6418-56cd-9ae7-cb209df8fec1
task_key
test--713d7efc-6418-56cd-9ae7-cb209df8fec1
task_revision_id
1
config / split
/ test

Official source

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