All sides of $\triangle ABC$ are tangent to circle $P$.
**What is the perimeter of the triangle below?**
[[☃ numeric-input 1]] units
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[Harder version, requires minor algebraic reasoning.
web+graphie://ka-perseus-graphie.s3.amazonaws.com/f965949ceb8d6e18a92c062ee0b635e68d36caec]: