Cho tam giác ABC vuông tại C. Trên BC, lấy điểm D sao cho AB = 13 cm, AP = OQ. Từ điểm A, vẽ AM song song với BC

Based on the triangular problem you provided, let's break down the tasks one by one:

1. **Find the length of CD in the trapezoid (hình 1)** given:
- \( AB = 9 \) cm
- \( AD = 4 \) cm
- \( BC = 5 \) cm

To find \( CD \), you can use the properties of trapezoids. Since \( AB \) is parallel to \( CD \), you can apply the formula for the area of the trapezoid or use the Pythagorean theorem depending on the specifics given.

2. **The task involving triangle ABC**:
- You have a right triangle where \( C \) is the right angle, with \( AB = 13 \) cm, \( AC = ? \), and \( BC = 15 \) cm.
- To find \( AC \), you can apply the Pythagorean theorem:
\[
AB^2 = AC^2 + BC^2
\]
Substitute the values and solve for \( AC \).

3. **The triangle AMB**:
- Since \( AM \) is parallel to \( BC \), triangle AMB will be similar to triangle ABC. You can use this relationship between the sides to determine ratios or other triangle properties.

Feel free to ask if you need assistance with specific calculations!