==> geometry/bisector.s <==
PROVE: XE.
Then ang(PDX) < ang(QEX)
Now considering triangles BXD and CXE,
the last condition requires that
ang(DBX) > ang(ECX)
OR ang(XBC) > ang(XCB)
OR XC > XB
Thus our assumption leads to :
XC + XD > XE + XB
OR CD > BE
which is a contradiction.
Similarly, one can show that XD < XE leads to a contradiction too.
Hence XD = XE => CX = BX
From which it is easy to prove that the triangle is isosceles.
-- Manish S Prabhu (mprabhu@magnus.acs.ohio-state.edu)