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MathNet 2020 — Math Olympiad Vault — Part 01 Question 118

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 01

Question 118

Suppose all the edges of regular triangular pyramid $P$-$ABC$ have length $1$ and $L$, $M$, $N$ are the midpoints of edges $PA$, $PB$ and $PC$, respectively. The area of the cross section of the circumscribed sphere of this regular triangular pyramid intercepted by plane $LMN$ is ______.