As shown in figure 1, when point m moves to point M 1 which is symmetrical with point c ABout ab, quadrilateral AMBC is an axisymmetric figure.

The length AM 1 of ∴ arc is 60 π× 4 180 = 43 π, ∴t 1=43s(3 points).

As shown in fig. 2, when the point m moves to the point M2, the quadrilateral AMBC is a rectangle.

∴ the arc length AM2 is:120 π× 4180 = 83 π ∴ T2 = 83s (6 points).

As shown in fig. 3, when the point m moves to the point M3, the quadrilateral ABMC is an isosceles trapezoid.

The length of arc ABM3 is: 240 π× 4 180 = 163 π, ∴t3= 163s(8 points).

∴ When t=43s, 83s or 163s, the quadrilateral with vertices A, M, B and C is an axisymmetric figure.