A difficult problem with easy solution | problem on intersecting chords

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I had a different solution but I liked yours more. I added a line from O (the center) to the midpoint of AB (I called this point E). I also added the line AO with length 7. Because AE is half of AB, AE = 6.5. By right triangle, 7^2 = 6.5^2 + OE^2. OE^2 = 6.75
Then again by right triangle, PO^2 = OE^2 + PE^2, or 3^2 = 6.75 + PE^2. PE = 1.5. This means PB = 1.5 + 6.5 = 8
PB = 8 and AP = 5.

jhawk
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I have different solution which is more simple

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