Yohan C. answered • 04/03/15

Tutor

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Math Tutor (up to Calculus) (not Statistics and Finite)

Hi Laxman,

It looks like you have an image like this:

If horizontal chord is AB and vertical chord is CD, then it will be a square for figure OMPN.

From what I've observe, the diameter will be √2 times the leg.

From this perspective, midpoint of each leg is 0.5 or 1/2 of original length (1 or x). And midpoint of diameter (hypotenuse) will be √2/2. From here, you have to calculate the new lengths of each leg to see if they add up to half of diameter (hypotenuse) (a

^{2}+ b^{2}= c^{2}) and to see if each leg are perpendicular or form a right angle. Basically, you will have a square inside of 45-45-90 triangle.(leg 1)

^{2}+ (leg 2)^{2}= (diameter/2)^{2} a

^{2}+ b^{2}= c^{2}(0.5)

^{2}+ (0.5)^{2}= (√2/2)^{2}0.25 + 0.25 = (2/4) = 1/2

0.5 = 1/2 It works.

How about with an x?

(x/2)

^{2}+ (x/2)^{2}= (x√2/2)^{2}(x

^{2}/4) + (x^{2}/4) = (2x^{2}/4) = (x^{2}/2)2x

^{2}/ 4 = x^{2}/ 2x

^{2}/ 2 = x^{2}/ 2 It works as well.I hope you got it.

Yohan C.

04/03/15