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Problem of the Week
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.

Rectangle ABCD with point P in its interior. AP is 5 units
long, BP is 11 units long, and DP is 10 units long.

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.