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Unsolved Challenge Prove ∠PAB = ∠CAQ

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MHB POTW Director
Staff member
Feb 14, 2012
The insphere and the exsphere opposite to the vertex $D$ of a (not necessarily regular) tetrahedron $ABCD$ touch the face $ABC$ in the points $P$ and $Q$, respectively. Show that $\angle PAB=\angle CAQ$.