Chord ac intersects chord bd at point p in circle z.

ap=3.5 in.
dp=4 in.
pc=6 in.

what is bp?

1. To solve this problem and find the value of BP, you must apply the "Intersecting chords theorem".

 2. You have that:

 AP=3.5 in
 PC=6 in
 DP=4 in

 3. Then, by applying the "Intersecting chord theorem", you have:

 (AP)(PC)=(BP)(DP)

 4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:

 (3.5 in)(6 in)/BP(4 in)

 5. Now, you must clear BP. Then:

 (3.5 in)(6 in)/4 in=BP
 21 in^2/4 in=BP

 6. Therefore, the value of BP is:

 BP=5.25 in