Meylani is a genius... but his book is crazy hard

Test Preparation SAT Subject Test Preparation
1

<p>If anyone could explain how to get this answer to me, I would greatly appreciate it. </p>

<p>For those of you who have the book, it's number 28 on page 39. I understand how to get BC and AB, but am drawing a blank for determining AC.</p>

<p>If you don't have the book, this is how the question goes:
1. The Diagram: Draw a circle. Now draw the center point. Now draw two radii from the center point down to two points on the circle. This should result in an isoceles triangle. Label the intersections of the radii and the circle B and C (going from left to right). The center angle of the triangle formed has a measure of alpha (I'll just call it "a"). Now draw another point on the circle above B and C and call it A. Draw lines from B to A and from C to A. You should come up with something vaguely resembling a star trek logo inscribed inside of a circle.
2. The Question: If B and C are fixed, but A can be moved anywhere between B and C (on the circle), what formula gives the perimeter of triangle ABC.
3. What I know: AB = (2)(r)(cos(x)); BC = (2)(r)(sin(a/2))
4. What I don't know: AC</p>

2

<p>what's x?</p>

<p>" AB = (2)(r)(cos(x)); "</p>

3

<p>Wow, I'm sorry - I left out one of the most important variables. X is the angle between triangle ABC and the triangle formed by BC and the center of the circle. This angle is on the left side of the diagram, so I suppose one could say it's the inside of the left "leg" of the star trek logo.</p>

4

<p>AC=2rcos(a/2-X) basically the angle of the "right leg" is a/2-X, remember angel BAC=a/2</p>

5

<p>OK, I think that I know what's going on now. Thanks</p>