# Squishing a Semi-arc

Geometry Level 4

An arc is suspended between two lines at fixed points $$A$$ and $$B$$ on the line such that segment $$AB$$ is perpendicular to both of the lines. The arc has length 100 units and segment $$AB$$ has length 90 units. The two lines move closer and closer at a rate of 2 units per minute, thus squishing the arc. After how many minutes does arc $$AB$$ no longer become an arc?

Details and assumptions

• Arc $$AB$$ obeys physical properties, and bends in the most natural way possible

• Arc $$AB$$ never goes through either of the lines suspending it

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