Pythagoras theorem

  Eargasm 23:20 14 Feb 05

Ok all, not strictly a pc question but this has been bugging me for a while,can anyone explain (in simple terms) how to get to line 4 and 5 of the formula from line 3.(the bit after or)
I understand the factorising bit ,but i am at a loss with line 4.

I hope f.e. allows this post as i know it's not pc related.

At work i develop many patterns using trigonometry and triangulation, but on first viewing of the puzzle i would of said there was'nt enough info to find the here Thanks

  HappySoul 23:32 14 Feb 05

Square 3 and 4 add together to get 5.

Square 5 and take away the Square of 3 (or 4) to give you the square of 4 (or 3).

  HappySoul 23:33 14 Feb 05

Sorry, I think I misunderstood you.

  Eargasm 23:35 14 Feb 05

I think my link may not take you to the solution
you may have to click on "score and show answers"


  justme 06:59 15 Feb 05

the generic formula for simplifying (a - b)² is

A² + 2ab + B²

Does this help at all?

  Simsy 08:05 15 Feb 05

how do you get from;

(r - 3)squared + (r - 6)squared = r2


r2 - 2(3)r + 32 + r2 - 2(6)r + 62 = r2

If that's what you mean, then, for example;

(r - 3)squared is (r-3)x(r-3)

you need to multiply each bit within each bracket by each bit within each bracket... so

Multiply the first "r" by the second "r"

Multiply the first "r" by the second "-3"

Multiply the first "-3" by the second "r"

Multiply the first "-3" by the second "-3"

This gives;

"r"squared -3r -3r +9

which is the same as

"r"squared -6r +9

which is the same as

"r"squared -2(3r) +9

and so on...

Does that help?

Apologiesd if I've got the wrong end of the stick.



  badgery 08:15 15 Feb 05

Surely " -2ab " in your formula!

And, yes , Eargasm, there is plenty of info to get the answer. Draw a line from centre of circle to point of contact with rectangle. Form a right angled triangle, with the radius line as hypotenuse, and apply Pythagoras theorem to it, (using 'x' as the radius length). Ensuing quadratic equation can then be solved to give two answers - one of which is impossible, so other is correct !
Or, there may be shorter way......!!??

  badgery 08:21 15 Feb 05

Sorry, the reference to the -2ab formula was for justme - simsy 'sneaked in' before I had sent reply!!

  gedr 16:04 15 Feb 05

If my memory serves me right, isn't it, the square of the hypotenuse is equal to the sum of the squares of the two remaining sides?


  justme 16:19 15 Feb 05

You are of course quite correct. My only excuse was that it was very early in the morning and my typing fingers had not woken up ;-)

  rawsongreen 17:15 15 Feb 05

(r-4)²+(r-8)² is

(r-4)(r-4) + (r-8)(r-8) Multiplied out this becomes

r²-4r-4r+16 + r²-8r-8r+64 This is the same as the line after 'or' eg 2x4r=8r

=2r²-24r+80 and a quadratic equation does the rest

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