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Omni-MATH / In equilateral triangle ABC, a circle …A to point D on segment BC such that AD intersects …E and F. If EF=4 and AB=8, determine |AE−FD|.

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problem

In equilateral triangle ABCA B C, a circle \omega is drawn such that it is tangent to all three sides of the triangle. A line is drawn from AA to point DD on segment BCB C such that ADA D intersects \omega at points EE and FF. If EF=4E F=4 and AB=8A B=8, determine |AE−FD||A E-F D|.
Plain-text mathematical notation (without MathML)
In equilateral triangle ABC, a circle \omega is drawn such that it is tangent to all three sides of the triangle. A line is drawn from A to point D on segment BC such that AD intersects \omega at points E and F. If EF=4 and AB=8, determine |AE−FD|.
Original LaTeX notation
In equilateral triangle $A B C$, a circle \omega is drawn such that it is tangent to all three sides of the triangle. A line is drawn from $A$ to point $D$ on segment $B C$ such that $A D$ intersects \omega at points $E$ and $F$. If $E F=4$ and $A B=8$, determine $|A E-F D|$.

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Source and history

task_id
6547bd89-9e55-533c-9dbb-934c141bd226
task_key
test--6547bd89-9e55-533c-9dbb-934c141bd226
task_revision_id
1
config / split
/ test

Official source

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