Inscribed angle? Cone angle? I need help please.

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LaoTse1

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Nov 16, 2019
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I have absolutely no clue how to even start with this.
Could anyone help me along with this, with possibly an step by step explanation and formula so that I could try to understand what's going on.
Any material or info about this subject would also be much appreciated.


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Please state the problem in words (the original words, if possible) and tell us the context. Where does this come from, and what topic is being studied, if any?

Are the handwritten numbers known, or are they part of your work? (They appear to be the result of incorrect thinking.) Is it known that all four circles have the same diameter? And so on.

It troubles me that the top line, AB, appears to be at an unknowable height above the top circles, so the 38 and 19 measurements may be useless. But if, as I think, they are wrong, then there is no problem.

In general, I would start by drawing in radii from the center of each circle to the points of tangency, then label distances that can be deduced. Many angles in the resulting figure will be equal.
 
Here is a specific suggestion:

Ignore the points you called A, B, C, and D. Use those names for the centers of the four circles, going clockwise from the upper left (near your A). They form an isosceles trapezoid ABCD. Find the lengths AB and CD, and the height of the trapezoid.

Now draw a vertical line from C to form a right triangle BEC. What are its sides? What angle can you find that will be useful?
 
Hi, thank you very much for answering.
A little background, I had a traffic accident 2 years ago and now unable to proceed my career as electro-mechanic. Going back to school to study industrial drawing.
My current "professor" hasn't given a single lesson in a month, just gave us a book we had to finish...

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I'm Belgian, so the coursework is in dutch.
Just finished the exercises with the cos, sin, tan and all its formulas. Adjacent side, opposite side,...

You are correct, the numbers written are mine. The diameters of the circles I assume are all equal.

I tried dividing the drawing into triangles which I know how to calculate...to no succes.

Here is the original
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I believe you mean [MATH]\alpha = 2\arctan(8,5/40)[/MATH]. I could see from the drawing that you had all the pieces in place. Good work!

Problems like this can be puzzles, in which you have to find the relevant relationships. I occasionally tutor students from this sort of course, and they have much more complicated problems than our trigonometry students.
 
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