Geometry puzzle

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ceptimus
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Geometry puzzle

Post by ceptimus »

What is x?

geometryPuzzle.gif
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Abdul Alhazred
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Re: Geometry puzzle

Post by Abdul Alhazred »

I'll try later.

First line of attack will be to extract the Pythagorean theorem from that diagram somehow.
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Bruce
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Re: Geometry puzzle

Post by Bruce »

Interesting. The answer must be between 6 and 10. Depends on the degree of overlap in the x and y directions and diameters of the circles. Looks like the degree of overlap in the y direction is 2, but I haven't found a way to solve the other three parameters. Will have to chew on it some more later.
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Rob Lister
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Re: Geometry puzzle

Post by Rob Lister »

pffft. I just measured. It's 8
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robinson
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Re: Geometry puzzle

Post by robinson »

Yep

Because it’s a square
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Re: Geometry puzzle

Post by robinson »

The way it’s presented is a trick

It’s the square encompassing the two circles
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ceptimus
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Re: Geometry puzzle

Post by ceptimus »

Nope. It's not a square. There's no trick.

Break out your drawing instruments and draw it as accurately as you can - then you can measure x to a decent degree of accuracy.

Those of you who know how can draw it using a CAD program, and so measure x very accurately.

But the best way is to use mathematics or geometry. It's not that difficult.
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Re: Geometry puzzle

Post by Anaxagoras »

By eyeball x > 8.

Can we assume all angles are right angles?

I don't understand the significance of the line segment of length 6. Is it given that this line is parallel to the others? I.e., that the vertical lines are all parallel and the horizontal lines are perpendicular to the vertical lines? Can we further assume that the line segment of length 6 passes through the point where the two circles touch?
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robinson
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Re: Geometry puzzle

Post by robinson »

It has to be a square
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Re: Geometry puzzle

Post by robinson »

If you square a circle then add another circle, and square them both, its always a square
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Re: Geometry puzzle

Post by robinson »

I could be wrong

It’s not 8

But it looks like a square
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ceptimus
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Re: Geometry puzzle

Post by ceptimus »

Anaxagoras wrote: Wed Sep 16, 2020 10:30 am By eyeball x > 8.

Can we assume all angles are right angles?

I don't understand the significance of the line segment of length 6. Is it given that this line is parallel to the others? I.e., that the vertical lines are all parallel and the horizontal lines are perpendicular to the vertical lines? Can we further assume that the line segment of length 6 passes through the point where the two circles touch?
Yes x > 8.
The outer rectangle is a true rectangle (right-angled corners and straight sides) with short side length 8.
The two circles are true circles. They touch each other tangentially (just touch without overlapping). One circle tangentially touches one short side and one long side of the rectangle, the other circle tangentially touches the remaining two sides.
The line shown with length 6 is parallel to the short sides of the rectangle. The line's ends are points on the circles, and the line passes through the point where the circles touch.
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Re: Geometry puzzle

Post by robinson »

I know the answer but I cheated. Yeah, not a square
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Abdul Alhazred
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Re: Geometry puzzle

Post by Abdul Alhazred »

Ten. :)
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ceptimus
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Re: Geometry puzzle

Post by ceptimus »

Abdul Alhazred wrote: Wed Sep 16, 2020 2:20 pm Ten. :)
Good guess...
Spoiler:
but wrong. :D
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Re: Geometry puzzle

Post by Anaxagoras »

Yeah, there may be some principle of geometry that allows one to solve for x, but I don't know what it is.
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ceptimus
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Re: Geometry puzzle

Post by ceptimus »

Anaxagoras wrote: Wed Sep 16, 2020 3:30 pm Yeah, there may be some principle of geometry that allows one to solve for x, but I don't know what it is.
Most people would agree that the Pythagorean theorem is a fundamental part of geometry. As Abdul suggested, the trick with most of these sorts of puzzle is to draw a few lines and then apply Pythagoras. The real trick is to know which lines to draw!
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Abdul Alhazred
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Re: Geometry puzzle

Post by Abdul Alhazred »

ceptimus wrote: Wed Sep 16, 2020 2:45 pm
Abdul Alhazred wrote: Wed Sep 16, 2020 2:20 pm Ten. :)
Good guess...
Spoiler:
but wrong. :D
:cry:
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Re: Geometry puzzle

Post by shemp »

Interesting that ceptimus posted this over at ISF this morning and had two correct answers in less than an hour. I'll draw no conclusions.
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Anaxagoras
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Re: Geometry puzzle

Post by Anaxagoras »

Without looking for the answer I'm going to guess that it's 9, but I can't show my work.

Either that or it's not a whole number.
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