2002 AMC 10P Problem 16

Two walls and the ceiling of a room meet at right angles at point P. A fly is in the air one meter from one wall, eight meters from the other wall, and nine meters from point P. How many meters is the fly from the ceiling?

\text{(A) }\sqrt{13} \qquad \text{(B) }\sqrt{14} \qquad \text{(C) }\sqrt{15} \qquad \text{(D) }4 \qquad \text{(E) }\sqrt{17}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.