No can you please solve this in terms of Theorem 1 of proportional Thereom

To solve this problem, we will use the Basic Proportionality Theorem (BPT), also known as Thales's Theorem, and properties of similar triangles.

Step 1: Determine the ratio $AB : BC$.
We are given $BC = \frac{3}{8} AC$.
Since $A, B, C$ are collinear, $AC = AB + BC$.
Substitute $BC = \frac{3}{8} AC$ into the equation:
$AC = AB + \frac{3}{8} AC$
$AC - \frac{3}{8} AC = AB$
$\frac{5}{8} AC = AB$
So, $\frac{AB}{AC} = \frac{5}{8}$.
From this, $