circle geo question :/ (1 Viewer)

wandering17 · Jul 11, 2015

17. Three equal circles with radius r are stacked as shown. Find the height of the stack. (There is a base line, two circles next to eachother touching, and then one between them on top)

How much of circle geo will be in trial anyways? :/

Thanks much appreciated

InteGrand · Jul 11, 2015

wandering17 said:
17. Three equal circles with radius r are stacked as shown. Find the height of the stack. (There is a base line, two circles next to eachother touching, and then one between them on top)

How much of circle geo will be in trial anyways? :/

Thanks much appreciated

$Consider the triangle formed by joining the circles' centres. This is an equilateral triangle with side length $2r$, and hence its height is $\sqrt{3}r$ (which you can show by Pythagoras' Theorem). This triangle's base is $r$ units above the ground and its top vertex is $r$ units below the top of the upper circle. Therefore, the height of the stack is $r+\sqrt{3}r + r =\left(2+\sqrt{3}\right)r$ units.$

sharoooooo · Jul 12, 2015

wandering17 said:
How much of circle geo will be in trial anyways? :/

3-5 marks usually, depending on difficulty

circle geo question :/ (1 Viewer)

wandering17

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InteGrand

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