How Do You Calculate the Length of a Chord and Tangential Line in a Circle?

[ChimM]

Homework Statement

Attached here is a diagram. My questions are, how to compute for the value of the chord? How to compute for the value of the tangential line? Please help.. Thank you in advance.

 

[BvU]

Oops, the template got lost. Programming error or accidental deletion? Here it is again: :)

Homework Statement

2. Homework Equations
3. The Attempt at a Solution [/B]

Also, you want to ask clear questions. "Value of a chord" is not very scientific: Economic value ? Color value ? In this case you want the length.
Seems to me that one needs the circle radius also to make sense of this ?

 

[ChimM]

Sorry about the template.

Homework Statement

Problem statement: [/B]
Find the value of the chord (blue line) and at the same time the value of the tangential line.

Given data:
Red line = 6
Green Line = 3
Radius of the Circle = 2

Homework Equations

I don't know any equations that can solve the problem :(

The Attempt at a Solution

I used the area of a trapezoid. But too many unknown.

 

[BvU]

This help ? I see a way to calculate distance top left to center cicle, and then top left to tangent point.
And then there are isomorphic triangles to be found that can help us further...

 

[ChimM]

View attachment 75074
This help ? I see a way to calculate distance top left to center cicle, and then top left to tangent point.
And then there are isomorphic triangles to be found that can help us further...

From there, can I use pythagorean theorem to solve the value of the tangential line? :)

 

[BvU]

value being length, equation, whatever: yes, I should think so. Didn't work it all out in detail: your job. Finding a possible smarter way is also your job/challenge :)

 

[ChimM]

value being length, equation, whatever: yes, I should think so. Didn't work it all out in detail: your job. Finding a possible smarter way is also your job/challenge :)

Can you give me hints on how can I relate the length of the tangent line to the chord? Pleaseee. Thank you :)

 

[BvU]

Draw AD, calculate |AD|, calculate |AB| .
Look at isomorphic triangles ACE and DCE
then DCE and BCF
Looks like a lot of work. You do some too.

 

[ChimM]

View attachment 75076
Draw AD, calculate |AD|, calculate |AB| .
Look at isomorphic triangles ACE and DCE
then DCE and BCF
Looks like a lot of work. You do some too.

Hmm.. Since, the tangent line and Radius is perpendicular, then it creates a 90degrees. The other side is also 90degrees, would it be right if I use 45degrees for the chord line and the radius? :)

 

[BvU]

More questions, no work done yet. What about AD and AB?

 

[SSWheels]

Look at isomorphic triangles ACE and DCE

Hmmm ...
It seems that DCE isn't a triangle at all, since the 3 points are collinear!

 

[SSWheels]

View attachment 75074
This help ? I see a way to calculate distance top left to center cicle, and then top left to tangent point.
And then there are isomorphic triangles to be found that can help us further...

There are several assumptions made here:
1) The black lines are all tangent to the circle
2) The vertical tangent line, the red line, and the blue line are all parallel to each other
3) The green lines are perpendicular to the vertical tangent line
4) The red line bisects both green lines
5) The midpoint of the red line is collinear with the center of the circle and the tangent point of the vertical tangent line.

By "value of the tangent line," I assume he means the length of a segment of the vertical tangent line between the points where it intersects the other 2 tangent lines?
Also, the OP doesn't specify which tangent line

 

[BvU]

Hmmm ...
It seems that DCE isn't a triangle at all, since the 3 points are collinear!

Yes, sorry: DCB

Any results yet from the original poster ?

 

[ChimM]

Yes, sorry: DCB

Any results yet from the original poster ?

I used the tangent-chord theorem to get the length of the chord. Since 2 tangent lines created the chord, it formed a triangle. The chord as the base and the radius as the legs. As shown at the attached picture.

I used sine(45) to get the value of h. Sine 45 × 2 =h
h = 1.41
r - h = 2 - 1.41 = 0.59

Using pythagorean theorem:
2 = sqrt (X^2 + 0.59^2)
X = 1.91 = Half of the chord

2x = whole chord
2 × 1.91 = 3.82

Therefore, length of the chord is 3.82.

Please cite your corrections. Thank you :)

 

[BvU]

The 45 degrees is not correct. I don't understand the reasoning.

"Draw AD, calculate |AD|, calculate |AB| .
Look at isomorphic triangles ACE and DCB "

What did you get for |AD|, |AB| ? Angle EAC ? Angle DCB ? Angle DBF ?