Triangle-Line II

https://www.desmos.com/calculator/fhm4x0lctw

This problem is technically a bit more complex than the Grade 9 one, Triangle-line I, but we think grade 10 students would enjoy it. Basically what it asks you to do is solve two linear equations in the two unknowns t and T. Students have essentially done this before when they have found the intersection of two lines in the plane. But this is a new context.

As before, the ABC triangle moves between the A0B0C0 and the A1B1C1 triangles with the vertices following a straight line.

Again the triangle appears to flip over at some point and change its orientation and at that point it will be a line segment. Our job is to find the time T at which this happens.