1. First, it is proved that △ABC is a right triangle and ∠C is a right triangle by using the side length of the known triangle.

According to the parallelism condition, parallelism is established when △AQP is a right triangle and △ ∠PQA is a right angle.

Both AP and AQ can be expressed by expressions containing t,

Using the ratio of AP to AQ is equal to the ratio of AB to AC, an equation is established to solve T.

2. Use P for PD⊥AC and D for D.

PD can be expressed by an expression containing t (hint, pay attention to the ratio of AP to PQ)

AQ can be expressed by an expression with a T.

△ area of △AQP =AQ*PD/2,

Substituting into the formula containing T, the area of △AQP becomes a binary linear equation containing T.

The next step is to find the maximum value of parabola within the range of t value.

3. The expression of △ AQP area containing t has been calculated in the second question.

△ABC's area is easy to calculate.

Suppose PQ just bisects the area of △ABC.

Then the area of △AQP is half that of △ABC.

What follows is the same as the second question.