This problem outlines one of the shortest proofs of the Pythagorean theorem. The proof w...

This problem outlines one of the shortest proofs of the Pythagorean theorem. The proof was discovered by the Hindu mathematician Bha¯ skara (1114–ca. 1185). (For other proofs, see the next exercise and also Exercise 100 on page 79.) In the figure we are given a right triangle ACB with the right angle at C, and we want to prove that