Question

Help with chord lengths? Thanks!

Answer 1

I need help knowing how to find GE. I know the answer is \[20\sqrt{3}\] but I don't know how to find that answer!

Answer 2

Sorry, the final answer is actually \[20\sqrt{2}\]

Answer 3

\(DG^2 = DF^2 + FG^2\) [Because of Pythagorus' Theorem]
\(DF = FG\) [Given]
\(DG = 20\) [Given]

\(2GF^2 = 400\)
\(GF^2 = 200\)
\(GF = 10 \sqrt{2}\)

Because, the radius perpendicular to the chord also bisects it, \(GE = 2GF\)
Hence,

\(GE = 2 * 10 \sqrt{2}\)
\(GE = 20 \sqrt{2}\)

Answer 4

Thank you! But, why does 2GF^2 = 400? I get a little confused around there.

Answer 5

@AkashdeepDeb

Answer 6

\(DF = FG = GF\)
\(DF^2 + FG^2 = 2 * GF^2 = 2 * DF^2 = 2 * FG^2\)

Answer 7

Thank you! :D Can you help me find the measure of the arc AG in the same image? Also, I don't really understand the difference between the AG arc and the angle D. How do you transition between the two? Thanks!!

Answer 8

Angle D is just the angle. It is like the angle your clock is forming with the minute and the hour hand.
Arc AG is an actual length. It's the length of the arc if you place a string along the curve AD.

Answer 9

Wait, do you mean the curve of AG? AD doesn't curve.

Answer 10

What I mean is, you said, if you place a string along the curve AD. AD isn't a curve. Did you mean AG?

Answer 11

Also, does knowing the angle D help you find the arc AG at all?

Answer 12

Yes, I meant AG and not AD.

Also, yes, you do need to know angle D to find arc AG's length. Do you know how to find out angle D?

Answer 13

Yes, angle D is 90 degrees because angle GDE is 90 degrees and AE is the diametor which is 180 degrees. I do know basic ratios but have had a harder time working with them.

Answer 14

I mainly need help knowing how to find arcs and what information you need to find them.

Answer 15

You do not need trig. at all here. My bad.
You are right, D will be 90 degrees.

Answer 16

Do you know what the circumference is?

Answer 17

360 degrees

Answer 18

No, the length of the circumference is = \(2 * \pi * r\)
Where \(r\) is the radius. Here, 20.

So, find the circumference.

Aldo, if D is 90 degrees, it basically divides the entire circle into 4 equal parts (or 4 equal quadrants). Hence, the length of the arc AG can be found out by diving the circumference of the circle by 4. :)

Answer 19

Isn't the circumference the length around the whole circle?

Answer 20

Yes, it is.

Answer 21

Isn't that 360 degrees?

Answer 22

\[2*\pi*20\]

Answer 23

That's not the length. That's the measure of the angle.
Just like when it is 6 am, the minute hand and the hour hand form 180 degree between them, and that's just the angle measure.

The circumference of a circle is defined as the length of the distance around the circle.

Answer 24

But, yes, the angle of the circle is 360. That is, the whole circle!

Answer 25

oh okay. So the circumference is: \[2*3.14*20\]

Answer 26

Yes.

Answer 27

divided by 4 which is 31.4

Answer 28

Absolutely right!

Answer 29

And that's the length of arc AG.

Answer 30

These problems are just practice problems so i have the correct answers and it says it's 90 degrees. How do you change 31.4 to degrees?

Answer 31

I think you're getting confused here.

Angle and Length IS NOT the same thing, so you cannot CHANGE length to degrees.



I think, what they means is, the angle of the arc AG = 90 degrees. But the length of the arc AG = 31.4 units.