Note: P is on the diameter EF, AB⊥EF, so there is PA=PB, so AP+CP=BP+CP. Obviously, when P passes through the straight line BC, it is the smallest, and its length is equal to the length of BC.
In order to make BC the shortest, AB is the diameter of a circle (that is, AB⊥EF is both dazzling), and it is easy to find the diagonal BC = 56 (1/2) = 2 * root sign (14) in the isosceles trapezoid ABDC.
Graphics are not easy to insert, which is also a major drawback that Baidu knows, but I hope you can understand.