One Circle - Two Tangent Lines

G

gailplush

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Joined
Aug 6, 2010
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OK...I've been fooling wit this for a while & I think I'm close. My knowns:

Start Point & Endpoint of two intersecting lines & the radius of the circle.

The problem:

Find the tangent points.

My progress:

1. Use the points to calculate the slope
2. move b (intercept) to one side of the equation & use an X,Y & b to find the equations of the lines.
3. Find the intersection of the two lines.
4. Find the angle between the two lines.
5. Find the distance from the intersection point to the tangent point using the tangent function.
6. Use the formulas X2=X1+[cos(angle)*Distance], Y2=Y1+[sin(angle)*Distance] for my X & Y values..

Step six is off, per my Cad Package. Everything else is dead on. I'm not sure where I went wrong, or if I'm approaching this all wrong. Any help would be greatly appreciated.

Enter Known X & Y
Line 1
x1 y1 x2 y2
0 0 11 10
Line 2
x1 y1 x2 y2
0 10 10 0

Slope - Calculated

Line 1 0.909090909
Line 2 -1


Y intercept - Calculated

Line 1 0
Line 2 10


Intersection Points - Calculated

X Value 5.238095238
Y Value 4.761904762


Angle Between The Two Lines - Calculated

Angle/2 -43.6368445

Distance From Tangent Point - Calculated

Circle Radius Known

Radius 4

Distance From Intersection To Tangent Point - Calculated

Distance 4.19500877

New Coordinates - Calculated

X Value 2.202048897
Y Value 7.656817748


GP
 
Did you "rough graph" this?

Where is the circle? There's 4 possible locations, right?
There's 2 angles at intersection: ~87 (which you're using, I think) and ~93 : are you confusing them?

NOTE: I roughly graphed your info watching hockey game at same time, so....
 
I think the attachment answers most of the questions..I don't believe, I'm getting this confused, but I'll take another look. Let me know if this helps...

Thanks again,

GP
 
I went ahead and looked at the other solutions, and they don't match up to my numbers either...

GP
 
gailplush said:
The problem:
Find the tangent points.
............
New Coordinates - Calculated
X Value 2.202048897
Y Value 7.656817748
Click to expand...
Why "New Coordinates"?
There are 2 tangent points; why are you showing only 1?
Now that we can tell where the circle is, I make these 2 points APPROXIMATELY (2.5 , 7.6) and (2.2 , 2.0).
 
There is only one, because I figured I need to get that one right, before I worry about the second. The points need to be 2.2718, 7.7282 (per cad)...So, I'm slightly off. The unerlying formula to get what I confusingly labelled "new coordinates" is this :

X2=X1-[cos(angle)*Distance],
Y2=Y1+[sin(angle)*Distance]

Where distance is calculated from the intersection, which is calculated by using the equations for the lines. Everything matches up perfectly, except for the last step..So frustrating.

Am I approaching this all wrong?

GP
 
Well, I get same as you: (~2.2020, ~7.6568)

I used YOUR "calculations": angle ~87.2736 ; distance ~4.1950 ; int.point(~5.2381, ~4.7619)

Soooo.... 2 possibilities:
1: CAD is wrong
2: YOUR "calculations" are wrong (but close!) : I didn't check 'em
 
I found when I substituted 45 degrees in, I agree with Cad, which makes sense, because it is the "along" axis dimension I'm trying to find, although, I haven't completely made sense of it yet (in my head).

GP
 
Agree; all's fine if 45 degrees.
Perhaps there's a typo involved: point(11,10) should be (10,10) ?
 
No..I actually did that on purpose...It seems as if the math should work, no matter what. That is why I'm questioning my approach.

GP
 
gailplush said:
No..I actually did that on purpose...It seems as if the math should work, no matter what. That is why I'm questioning my approach.
Click to expand...
But WHY are you questionning your approach?
Your results SHOULD BE different from CAD's, since CAD was using (10,10), not (10,11) ... right?
Like, CAD would have intersecting point (5,5), right?
 
No...Cad had the same points...I think I've figured it out, i just need to work through it again.

GP
 
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