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Omni-MATH / In the Cartesian plane, a perfectly reflective semicircular room is bounded by…

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problem

In the Cartesian plane, a perfectly reflective semicircular room is bounded by the upper half of the unit circle centered at (0,0)(0,0) and the line segment from (−1,0)(-1,0) to (1,0)(1,0). David stands at the point (−1,0)(-1,0) and shines a flashlight into the room at an angle of 46∘46^{\circ} above the horizontal. How many times does the light beam reflect off the walls before coming back to David at (−1,0)(-1,0) for the first time?
Plain-text mathematical notation (without MathML)
In the Cartesian plane, a perfectly reflective semicircular room is bounded by the upper half of the unit circle centered at (0,0) and the line segment from (−1,0) to (1,0). David stands at the point (−1,0) and shines a flashlight into the room at an angle of 46^(∘) above the horizontal. How many times does the light beam reflect off the walls before coming back to David at (−1,0) for the first time?
Original LaTeX notation
In the Cartesian plane, a perfectly reflective semicircular room is bounded by the upper half of the unit circle centered at $(0,0)$ and the line segment from $(-1,0)$ to $(1,0)$. David stands at the point $(-1,0)$ and shines a flashlight into the room at an angle of $46^{\circ}$ above the horizontal. How many times does the light beam reflect off the walls before coming back to David at $(-1,0)$ for the first time?

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Source and history

task_id
d54ffbb1-5f78-5bc5-92d4-a1abd00e30ce
task_key
test--d54ffbb1-5f78-5bc5-92d4-a1abd00e30ce
task_revision_id
1
config / split
/ test

Official source

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