No solution exist.
NSolve[Rationalize[{eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10,
eq11, eq12}, 0], {xA, yA, xB, yB, xX1, yX1, xX2, yX2, xX3, yX3,
xX4, yX4}, Reals]
Reduce[Rationalize[{eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10,
eq11, eq12}, 0], {xA, yA, xB, yB, xX1, yX1, xX2, yX2, xX3, yX3,
xX4, yX4}, Reals]
Solve[Rationalize[{eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10,
eq11, eq12}, 0], {xA, yA, xB, yB, xX1, yX1, xX2, yX2, xX3, yX3,
xX4, yX4}, Reals, MaxExtraConditions -> All]