A friend, Teddy O'Connell, sent me this geometry problem he found on the Web, which is not too hard and has a pretty neat solution.
Let ABC be a right triangle, with a right angle at C. Suppose that a circle has been inscribed in the triangle (the incircle) which is tangent to ABC at one point on each side including the point D on the hypotenuse AB, such that |AD| = 3 and |DB| = 5. Find (ABC), the area of triangle ABC.
(drawing not to scale)
I will follow this posting with two comments. The first will contain a couple of hints, and the second (to be posted later) is my solution and a related question that I don't have an answer to.
