please suggest: geometry problem from GMATPrep

Hi, Sampolo

Can you please post the entire text of the question (and the answer choices)? What you have posted only says that one vertex of a triangle is at the center of a circle with radius 1. The lengths could be anything. Are the other two vertices on the circle itself or something like that?

Got it. So one vertex is at the center and the other two are on the circle itself. If we call the point at the center A and the other two B and C, AB will be 1 and AC will be 1 b/c both are radii of the circle.

As a rule, for any particular dimensions, you will maximize the area if you make the triangle a right triangle. This is because the two legs will then be the base and the height of the triangle (which matches the triangle formula: 1/2 * B * H). For a non-right triangle, the height will always be less than the length of the leg which would have been the height if this were a right triangle.

Try drawing some triangles, some right and some non-right. Anything other than 90 will result in the height equaling something less than 1. If we want to maximize, we want to use the largest numbers for B and H, hence we draw a right triangle and B and H are both equal to 1.

Yes, you can draw triangles that way too, but the areas will still be less than the area of the right triangle.

You can follow the below link if you want to read more. Generally, though, just know the rule that to maximize the area of an isosceles triangle, you need a right triangle. (This is no different than knowing, say, the Pythagorean theorem. You don't need to prove it on the test - you just need to know. The only different with this problem is that the rule is a bit more obscure.)

https://my.nctm.org/eresources/view_medi ... le_id=2073