My instinct on this is that the answer is D-- "cannot be determined." Since we all know that geometric figures cannot be assumed to be drawn to scale unless we're told that they have been, there's no way to know what type of triangle we're looking at, and that definitely affects how we calculate area. Isosceles? Scalene? Right? Equilateral? We don't know.

Look at it another way: what if the circle is 3cm in diameter but the bottom of the triangle actually stretches out for 3 miles? That's possible, right? If we assume, for the sake of argument, that the circle has a fixed radius-- 3cm or whatever-- and that we can circumscribe different triangles around it, then we get the same problem: there's an infinite number of possible triangles that can be circumscribed around that one particular circle.

I should note, too, that if the circumscribed triangle is equilateral, then the area of the circle will obviously be greater than the shaded area. If, however, one leg of the circumscribed triangle is 30,000 times longer than the radius of the inscribed circle, it should be obvious that the shaded area will be greater than the area of the circle. If what I've written is true, then there's no way to know which quantity, A or B, is greater without knowing more about the figure we're looking at.

## 1 comment:

My instinct on this is that the answer is D-- "cannot be determined." Since we all know that geometric figures cannot be assumed to be drawn to scale unless we're told that they have been, there's no way to know what type of triangle we're looking at, and that definitely affects how we calculate area. Isosceles? Scalene? Right? Equilateral? We don't know.

Look at it another way: what if the circle is 3cm in diameter but the bottom of the triangle actually stretches out for 3 miles? That's possible, right? If we assume, for the sake of argument, that the circle has a fixed radius-- 3cm or whatever-- and that we can circumscribe different triangles around it, then we get the same problem: there's an infinite number of possible triangles that can be circumscribed around that one particular circle.

I should note, too, that if the circumscribed triangle is equilateral, then the area of the circle will obviously be greater than the shaded area. If, however, one leg of the circumscribed triangle is 30,000 times longer than the radius of the inscribed circle, it should be obvious that the shaded area will be greater than the area of the circle. If what I've written is true, then there's no way to know which quantity, A or B, is greater without knowing more about the figure we're looking at.

So, yeah: I'm sticking with D.

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