In the following figure, points P and Q trisect the hypotenuse in ∆ABC. Prove that the squ...

In the following figure, points P and Q trisect the hypotenuse in ∆ABC. Prove that the square of the hypotenuse is equal to 9/5 the sum of the squares of the distances from the trisection points to the vertex A of the right angle.

Hint: Let the coordinates of B and C be (0, 3b) and (3c, 0), respectively. Then the coordinates of P and Q are (c, 2b) and (2c, b), respectively.