Hey Knight,

You know, I wouldn't spend too much time worrying about the "obscure" rules like that incircle rule. The GMAT doesn't have much incentive to reward memorization like that - it's definitely not a test of how much you remember from high school geometry, but rather of your ability to leverage what you know about basic geometry (areas, perimeters, Pythagorean theorem, the coordinate plane) to solve seemingly unique problems.

So much about GMAT geometry is about finding ways to apply the basic things that you do know to these problems. So, for example, in your first question, without knowing or applying that incircle rule I could still draw the circle inside the triangle and apply a few basics.

Area = 1/2 bh = 1/2 5 * 12 = 30
So the "height" from the hypotenuse to the right angle is going to be:

A = 30 = 1/2 bh = 1/2 (13)(h)
So 30 = 1/2 (13h)
60 = 13h
h = something between 4 and 5

Well, the diameter of that circle is going to be less than that height, as the circle can't fill that entire space between the hypotenuse and the opposite corner (draw it and you'll see). And since the radius is "half of less than 4.5" by that logic, 2 is the only possible answer.


So while formulas like that one can be helpful, the GMAT doesn't require you to know anything that obscure...there's always a logical way to get the answer by seeing ways to use the basics. And in that way the basics area "sustainable" - trying to remember (or relearn) everything from high school geometry just isn't worth the time...especially because you know that that's not the GMAT's intent anyway.

That said, I would try to remember that "diameter + any point on the outside of a circle = right triangle". Why? Because it's a perfect link between circles and right triangles, and you know that the GMAT likes to make you blend shapes. But as far as pure formulas (and not just concepts) go, you're in great shape with perimeter/area/Pythagorean/coordinate plane, and some ingenuity to see where you can use those effectively.

Brian@VeritasPrep great approach brian.....Its true and certainly logical way to solve that....

Knight- I did not know that formulae good to know that.....

Thanks mate