In quadrilateral ABCD the diagonals AC and BD cross at P, and the four pieces measure PA = 6 cm, PC = 4 cm, PB = 8 cm and PD = 3 cm. What follows from these measurements?

PA × PC = $6\times 4=24$ and PB × PD = $8\times 3=24$. By the converse of the intersecting-chords theorem, when two segments cross at a point and the products of their parts are equal, the four endpoints are concyclic — so one circle passes through A, B, C and D. The other options need extra facts the data does not supply: a parallelogram would require PA = PC and PB = PD, and AB ∥ DC would require PA : PC = PB : PD, but 6 : 4 is not 8 : 3.