Dr. Chung's SAT Math Question

Test Preparation
1

<p>hello! well first off, if anyone has the dr. chung's sat math book have the 50 tips at the beginning helped? i'm kind of on a time crunch so i don't want to go through them if they're not helpful. anyways my question:</p>

<p>Practice Test #1, Section 3, Question 4 (pg 98)</p>

<p>"In the figure above, a circle is tangent to the side of an equilateral triangle PQR and the radius r equals 5. what is the perimeter of PQR?"
there is a picture of an equilateral triangle and a circle inside of it. </p>

<p>Chung's explanation: perimeter is 30 root 3 he used the 30-60-90 triangle to find out the side. </p>

<p>my question is, how did he know the triangle was 30-60-90?</p>

2

<p>An equilateral triangle has 60 degree angles. If a line is drawn from the center of the circle to the triangle side, it makes a 90 degree angle. ergo, 30 60 90, that’s vashappenin.</p>

3

<p>@ParthivNaresh: I see how it makes a 90 degree angle, but how do you know its not say 28-62-90 or something random?
@IceQube haha thank you!</p>

4

<p>The line bisects the 60 degree angle. </p>

<p>–Edit–</p>

<p>Are you sure the answer is 30 root 3? I’m getting 30 + 10root3. Of course, my math could be rusty (it’s been some time since January …).</p>

5

<p>@IceQube don’t be mean to @ParthivNaresh. I happen to think ParthivNaresh is quite original. :slight_smile: @ParthivNaresh don’t let the haters get to you</p>

6

<p>How do you know the line bisects the 60? (my geometry skills are very rusty!)
and the explanation says half of one of the triangle sides is 5 root 3, so then the whole side is 10 root 3, so the perimeter is 3 x (10 root 3) which is 30 root 3.</p>

7

<p>Haha I take that back. It’s 30 root 3.</p>

<p>About the line: you make it bisect the 60. One angle has to be 90. Another one is 60. The last one has to be 30.</p>

<p>You can make it whatever you like, but one angle has to be 90. The radius is perpendicular to the side of the triangle. Make the other two angles 30 and 60 for convenience.</p>

8

<p>Alright now it finally makes sense in my head, thanks!</p>

9

<p>Wait, what? Somebody insulted me? I’ve got half a mind to hold my breath.</p>

10

<p>haha, no, no one insulted you ketone here was actually making fun of my name</p>

11

<p>can anyone explain tip number 27 in dr. chung’s for me?</p>

12

<p>@michellehby I can only see the “Paths in Grid” (since I’m looking at Amazon’s preview) but I think I know what they’re talking about.</p>

<p>For example, suppose you have a square grid of 16 dots (that is, 3x3) and you want to find the number of ways to get from the top left corner (A) to the lower right corner (B), by only moving right or down. Note that we have three “right” movements and three “down” movements that can be ordered in any way to produce a path. The number of paths is therefore 6C3 = 6!/(3!*3!) = 20. This method, of course, generalizes to any number of rows and columns.</p>

<p>There are other types of “paths in grid” problems but they’re too vague for me to give an explanation. If you have a specific problem, feel free to post/PM.</p>