5, 13, 15. Find the Missing Distance — The Rectangle Trick

A point is 5, 13 and 15 units from three corners of a rectangle. Find the fourth distance, then see why the same identity works even outside the rectangle. Opposite corners are A and C, and B and D. AP² + CP² = BP² + DP². The answer is 9. Includes a visual Pythagorean proof, moving-point demonstration, a parallelogram counterexample and a second puzzle. 0:00 Three distances, one missing 0:22 Pair opposite corners 0:50 The surprising balance 1:20 Turn four lines into triangles 1:47 The first opposite pair 2:12 The other opposite pair 2:40 Move P: the balance survives 3:08 Check the given numbers 3:36 What if P is outside? 4:09 Why not any parallelogram? 4:43 Your turn: find x 5:18 The rectangle does the work Original animation and explanation by Hidden WHY? Synthetic English narration. #Geometry #MathPuzzle #BritishFlagTheorem #HiddenWHY