Hello there. To solve this question, we have to remember some properties about circles and theorems relating chords.
Given the following diagram:
And the lengths of AP = 3.5, PD = 6 and PC = 4, we want to determine BP and BC.
Okay. First, we'll need the following theorem:
The theorem says that for the chords AC and BD, intersecting at E, it is true that

In this case, we have the lengths of three of the factors, therefore:

Plugging the values, we get

Divide both sides of the equation by a factor of 4

Finally, we know that

Hence we get

These are the answers to this question.