Problem D

Where is Pete?

Amir, Bita, Colin, and Delilah are standing on the four corners of a rectangular field, with Amir and Colin at opposite corners. Pete is standing inside the field \(5\) m from Amir, \(11\) m from Bita, and \(10\) m from Delilah. In the diagram, the locations of Amir, Bita, Colin, Delilah, and Pete are marked with \(A,~B,~C,~D,\) and \(P\), respectively.

Determine the distance from Pete to Colin.

Hint: Consider drawing a line segment through \(P\), perpendicular to two of the sides of the rectangle, and then using the Pythagorean Theorem.