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Omni-MATH / The walls of a room are in the shape of a triangle ABC with ∠ABC=90^(∘),∠BAC=60^(∘), and AB=6. Chong stands at the midpoint of BC and rolls a ball toward AB. Suppose that the ball …

Problem

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problem

The walls of a room are in the shape of a triangle ABCA B C with ∠ABC=90∘,∠BAC=60∘\angle A B C=90^{\circ}, \angle B A C=60^{\circ}, and AB=6A B=6. Chong stands at the midpoint of BCB C and rolls a ball toward ABA B. Suppose that the ball bounces off ABA B, then ACA C, then returns exactly to Chong. Find the length of the path of the ball.
Plain-text mathematical notation (without MathML)
The walls of a room are in the shape of a triangle ABC with ∠ABC=90^(∘),∠BAC=60^(∘), and AB=6. Chong stands at the midpoint of BC and rolls a ball toward AB. Suppose that the ball bounces off AB, then AC, then returns exactly to Chong. Find the length of the path of the ball.
Original LaTeX notation
The walls of a room are in the shape of a triangle $A B C$ with $\angle A B C=90^{\circ}, \angle B A C=60^{\circ}$, and $A B=6$. Chong stands at the midpoint of $B C$ and rolls a ball toward $A B$. Suppose that the ball bounces off $A B$, then $A C$, then returns exactly to Chong. Find the length of the path of the ball.

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Source and history

task_id
bdcc8eb4-80f5-5108-a32a-7d014185e02a
task_key
test--bdcc8eb4-80f5-5108-a32a-7d014185e02a
task_revision_id
1
config / split
/ test

Official source

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