Are Areas of Similar Circular Sections Proportional to Chord Squares?

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Homework Statement



Show that the areas of similar circular sections are proportional to the squares on their chords. Assume that the result that the areas of circles are proportional to the squares on their dimeters.

Homework Equations



no sure

The Attempt at a Solution



What does "squares on their chords mean" and "squares on their diameters mean"? I am having trouble visualizing what this is supposed to look like.
 
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read "squares on their chords" as "the square of the length of the chord"
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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