Please help me

Colleges and Universities A-Z Harvard University
1

<p>Hey Harvard students/prospies etc.!</p>

<p>Well, so I'm a junior in high school and right now I have a B+ (92.34 ...arghhhh!!) in my AP Calc class.</p>

<p>Since I'm so close to getting an A (less than .2 away), my teacher gave me this problem to do for extra credit and said that I could get any help I wanted (thank god, or I would never be able to do this).</p>

<p>So I've uploaded the problem online and you can see the problem here: <a href="http://i41.tinypic.com/10wutrc.jpg%5B/url%5D"&gt;http://i41.tinypic.com/10wutrc.jpg&lt;/a&gt;&lt;/p>

<p>The text for the problem is on the bottom and the diagram is the one on the right (exercise 28).</p>

<p>So I would really really really really really greatly appreciate it if one of you guys could figure this out and tell me how to do it (eg. where to draw auxilary lines, steps in proof).</p>

<p>Lol, i dont even get why I get a geometry problem for AP Calc but w/e.</p>

<p>So any help greatly appreciated! If you have any questions PM me! Please try to get this by tonight! </p>

<p>Thanks so much.
brainteaser955</p>

2

<p>I can give you a few hints and you can figure out the rest of it.

  1. BC is the diameter.
  2. CD^2=ED<em>AD
  3. AF</em>FE=BF*CF</p>
3

<p>Ok. So I just looked in my old geometry book and found out the reasons for #2 and #3…but I can’t get any farther. Can you please help me out and give me more hints/explanations! Thanks!</p>

<p>Gosh, I’ve been bogged down with a ****load of stuff, bunch of papers, etc. …</p>

<p>please help me as best as you can so I can get at least one thing out of the way</p>

4

<p>Also, How do you know that BC is the diameter?</p>

5

<p>Also, how do you get congruent triangles?</p>

6

<p>Any other takers that can help me out?</p>

<p>Thanks!</p>

7

<p>Sorry, I misinterpreted the question. My hints were wrong.</p>

8

<p>Sure, no problem. Thanks.</p>

9

<p>@happysunnyshine I tried sending you another PM but it says your inbox is full… oh and one more thing that may help: the two triangles are similar.</p>

10

<p>Since you know that the two triangles are similar, you can establish the two equations fairly easily.</p>

11

<ol>
<li>y^2=x*(x+16)</li>
<li>3/y=6/(10+x)</li>
</ol>

12

<p>right, so when i get 3/CD = 6/(10+X) , how do I go from there?</p>

13

<p>You have 2 variables and 2 equations.</p>

14

<p>oh lol sorry just saw you typed in the same thing</p>

15

<p>one sec</p>

<p>10char</p>

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<p>just PMed you, so my teacher told me the answer is 2. I just have to figure out how to get it. And i can’t get 2 with those two eqations</p>

17

<p>let ED=x and CD=y.
Let the midpoint of AB be M. Note that MC, being the perpendicular bisector of AB, contains O, the center. Because it contains O, it is thus perpendicular to the tangent CD </p>

<p>Hence, AB is parallel to CD. This easily implies that ABF is similar to CDF.</p>

<p>By the power of a point theorem: x(x+16) = y^2
By similar triangle ratios: 2y = 10+x
Hence y =6 and x = 2.</p>

18

<p>Check your calculation.</p>

19

<p>you said “Let the midpoint of AB be M. Note that MC, being the perpendicular bisector of AB, contains O, the center. Because it contains O, it is thus perpendicular to the tangent CD” …how do you know that MC is the perp bisector of AB? and how do you know it contains O?</p>

20

<p>anybody else out there that can help me understand what hrmph1 meant when he said “Let the midpoint of AB be M. Note that MC, being the perpendicular bisector of AB, contains O, the center. Because it contains O, it is thus perpendicular to the tangent CD” …how do you know that MC is the perp bisector of AB? and how do you know it contains O?</p>