12 x ? Rectangle in Bigger Circle. Am I Doing it Right?

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geekily

Junior Member
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Jan 24, 2007
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Ok, I drew a picture because I couldn't figure out how to explain the diagram. It's not great, but I think it gives you the general idea:

"find x"
math.jpg


The stuff in black is what I was given, red is what I've filled in. I figured by drawing that red line I could do Pythagorean Theorem, and then prove the triangles similar: The right triangle is in both of them, and they each have a bisected right angle, so they're similar, I believe. Then I can set up a comparison? We've been doing AB/DE = BC/EC = AC/DC, so I thought it might be that. However, I have no idea if that's even remotely on the right track, so before I go any further, can you please tell me if I'm doing it right?
 
geekily said:
We've been doing AB/DE = BC/EC = AC/DC...
Click to expand...
I'm sorry, but anybody who hasn't been working out of your particular textbook won't know what this means. :oops:

Note: Since this is a rectangle, since the diagonal drawn from the circle-center to the upper right-hand corner is also a radius line, and since the (right) triangles formed by that diagonal are equivalent to the triangles formed by the given diagonal, you have two of the sides of the right triangle. Use the Pythagorean Theorem to find the length of the third side. :D

Eliz.
 
Oh, I'm sorry! My teacher kept referring to it like it was a formula or something. What I mean, is, if you have 2 triangles and you know they are similar, you can match up the segments (AB of triangle ABC and DE of triangle DEC, for instance) and make ratios if you only know the length of some of them, because they will all be proportional, and you can use that to figure it out.

Are you saying that instead of using the 15^2 + 12^2 I should bring my diagonal over more and make it 15^2 + 15^2 = sqrt(450)? If so, how will that help me to find the length of x? I'm sorry, I'm just so confused - it's not your explaining, it's just me. :oops: Thanks for all your help!

Edit: Oh, I guess I found one of my mistakes, which is that diagonals of a rectangle don't bisect the vertices. I'm still lost, though.
 
You have a rectangle - whose diagonals are equal.

You are given one diagonal of length 'x' - you need to find length of this diagonal.

Draw the other diagonal by joining the center of the circle and the upper right hand vertex of the rectangle.

Don't just stare at the response - draw it.

Now do you see that this diagonal that you have drawn above also "a radius" of the circle.

Now then you have:

x = radius = 15
 
Oh, wow, it was that simple? I've been staring at this thing for like an hour and a half, haha. I wonder why it would even bother telling me the length of the triangle is 12, then.

Thank you so much for your help!
 
Hello, geekily!

This is classic trick question.

You're supposed to get involved with the Pythagorean Theorem, slopes.
. . distances, angles, etc.

Then kick yourself when you see the solution.

 
Haha, that is a very, very, very mean trick question. I'm just glad I asked or I'd probably still be staring at it now. :p
 
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