Find the Radius (Yet another puzzle)

[mendhak]

The rectangle in the corner is 2cm * 4 cm. Find radius of the circle.

[krtxmrtz]

Circle: x² + y² = r²

The rectangle point touching the circle has coordinates

-(r - 4), (r - 2)

Substituting:

(r - 4)² + (r - 2)² = r²

and this leads to

r² - 12r + 20 = 0

which has the roots 2 qnd 10. Obviously 10 is the correct answer.

[mendhak]

On the right track, but not quite there

[krtxmrtz]

Originally posted by mendhak
... but not quite there

Whaaaaaaat??????

[opus]

I can't wait to see, why 10 should not be the correct answer!
You did ask for radius, right!

[mendhak]

:embarassed:

Oh damn...

I was performing the calculations using 4cm * 8 cm :very embarassed:

OK, OK... the answer is 10.

[krtxmrtz]

What that means is you should pay more attention to the derivation itself than to the final numbers. Question: were you smoking at the time you figured that out?

[mendhak]

Why, yes. Yes I was.

I'll pay more attention next time. I'll be back with a tougher puzzle. Hopefully, you won't be able to solve it and will come crawling to me, BEGGING for a hint.

[krtxmrtz]

Originally posted by mendhak
Why, yes. Yes I was.

I'll pay more attention next time. I'll be back with a tougher puzzle. Hopefully, you won't be able to solve it and will come crawling to me, BEGGING for a hint.

I'm all agog waiting for the next one to come. My face is looking like in the old days when I was broke, used to smoke and ran out of cigarettes.

[prog_tom]

it was obvious.... did it in like 14 seconds,

there are 5 rectangles of length 4 cm in the big square, thus, 4 * 5 would be 20cm, the square has an area of 400cm^2,

so, 20/2 would give you the radius, which is 10cm.

[opus]

14 seconds, after 15 days cool!

[da_silvy]

Originally posted by prog_tom
it was obvious.... did it in like 14 seconds,

there are 5 rectangles of length 4 cm in the big square, thus, 4 * 5 would be 20cm, the square has an area of 400cm^2,

so, 20/2 would give you the radius, which is 10cm.

What if it was not to scale?

[prog_tom]

then there would be no correct way of finding the Correct radius.

[da_silvy]

Originally posted by krtxmrtz
Circle: x² + y² = r²

The rectangle point touching the circle has coordinates

-(r - 4), (r - 2)

Substituting:

(r - 4)² + (r - 2)² = r²

and this leads to

r² - 12r + 20 = 0

which has the roots 2 qnd 10. Obviously 10 is the correct answer.

This would still give the correct answer.

[prog_tom]

well that's because it's scaled,

it's just that it supposes the radius is r.

[krtxmrtz]

Originally posted by prog_tom
well that's because it's scaled,

it's just that it supposes the radius is r.

I think it's a sound assumption... If the radius is not r, then call it any name you like...
Honestly I don't understand what you mean.