Find the radius of the circle shown in the given figure.

[Cskenox]

Okay, so my history regarding math is borderline pitiable-- due to anxiety disorder I wasn't able to attend much schooling. I was in and out of various programs (many of them "alternative") and due to this I missed an incredulous amount of crucial math. To make matters worse I'm supremely right-brained; hence my aptitude with words and juxtaposing platitude in most left-brain persuasions.

I'm now taking a college math class, wherein I'm struggling...to say the least.

...but I digress, onto the math!

In this equation, I know I must find the radius. I tried writing down a few formulas that seemed relevant when I consulted the almighty google about this problem.

But to be completely honest, I don't even know where to start. Someone told me I should draw an "x" through the rectangle and find the correlation between the rectangle and the circle once I've done so...I don't understand why this would solve a radius problem, since rectangles can't be calculated for radii.

My goal is to not only know how to solve this, but to have the methodology behind solving it so that I can follow those steps with unerring accuracy and reproduce a correct result in future problems.

Thanks in advance!

 

[pka]

View attachment 1327

From the diagram we see that \(\displaystyle x^2+y^2=8^2\).
But that is the equation of that circle. So what is the radius?

 

[soroban]

Hello, Csknox!

This is a classic (very old) trick question . . .

I assume that a rectangle is inscribed in one quadrant of the circle.

The diagonals of a rectangle are equal.

We see that one diagonal is 8 units.
Hence, the other diagonal is also 8 units.

And the "other diagonal" is a radius of the circle!

 

[Cskenox]

Jeff, Pka, Soroban, thanks!

I understand haha, but only about 90%. I see that the rectangle contains two diagonals which are undoubtedly congruent with one another, but how is it that the other diagonal is the radius of the circle itself? especially when it only occupies one quadrant of the circle?

I apologize for the ignorance, but I just want to make sure my head is wrapped around this concept properly.

**Edit**

upon further examination I believe I get it now. The bisecting diagonal that I drew through the rectangle starts at border of the circle, and ends in the middle...thereby giving me the radius with the information present. Thanks to JeffM for elaborating.

I'll undoubtedly need more help in the future, but I'm making the effort to ingrain these concepts into my head so I can start doing this kind of stuff without assistance. I want to get to the point where I know exactly what to do and how to do it with any given mathematical problem...I've a long journey ahead of me, but all of you are very much an inspiration to my cause.

Thanks again .

 

[burakaltr]

View attachment 1327

Okay, so my history regarding math is borderline pitiable-- due to anxiety disorder I wasn't able to attend much schooling. I was in and out of various programs (many of them "alternative") and due to this I missed an incredulous amount of crucial math. To make matters worse I'm supremely right-brained; hence my aptitude with words and juxtaposing platitude in most left-brain persuasions.

I'm now taking a college math class, wherein I'm struggling...to say the least.

...but I digress, onto the math!

In this equation, I know I must find the radius. I tried writing down a few formulas that seemed relevant when I consulted the almighty google about this problem.

But to be completely honest, I don't even know where to start. Someone told me I should draw an "x" through the rectangle and find the correlation between the rectangle and the circle once I've done so...I don't understand why this would solve a radius problem, since rectangles can't be calculated for radii.

My goal is to not only know how to solve this, but to have the methodology behind solving it so that I can follow those steps with unerring accuracy and reproduce a correct result in future problems.

Thanks in advance!

r=8 units