How to Find the Length of a Chord in a Circle | Geometry, Circle Chords, Chord Length

How do we find the length of a chord in a circle? We go over circle chords, and how to find their length, in today's video math lesson!
Geometry sure is a blast! Today we get to go over trigonometry and sine ratios, we get to touch on right triangles, the isosceles triangle theorem, the hypotenuse leg congruence postulate for right triangles, central angles subtended by chords, and more! What a hoot!
If we have a chord of a circle with radius r, and the central angle subtended by that chord has a measure of A, then the length of the chord is 2*r*sin(A/2). We derive this formula, and go over an example of how to use it, in the video lesson. By understanding where it comes from, it is easy to recall!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
********************************************************************
The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: vallow.bandcam...
Vallow Spotify: open.spotify.c...
Vallow SoundCloud: / benwatts-3
********************************************************************
+WRATH OF MATH+
◆ Support Wrath of Math on Patreon: / wrathofmathlessons
Follow Wrath of Math on...
● Instagram: / wrathofmathedu
● Facebook: / wrathofmath
● Twitter: / wrathofmathedu
My Music Channel: / seanemusic

[@Sudi-nf3wp]

Best introduction to a maths video ever

[@mharunrasyid]

thank you very much to create this video 🤩, its very helpful for me

[@joewest1972]

I have a circle with a circumference of 46 inches. I think finding the diameter means divide 46 by pi (3.14) or 14.64 divided by 2 equals a radius of 7.325. Now stand the circle up and picture measuring up 3 inches from bottom dead center of the circle, now draw a chord at that point parallel to the diameter. How long is that chord?

[@internationalgolfconstruction]

Do you have any educational videos that walk us through the steps that Hipparchus used to make chord tables? I’m guessing that a series of videos walking us through how trigonometry was developed from the pyramids to Taylor series would be phenomenal.

[@ThatOneRo0ky]

thank you so much my math teacher never really talked about this in class and it is on the test tomorrow now i’m confident

[@Trident_Euclid]

Thank you so much. This will help me alot in the machine shop.

[@WrathofMath]

That's awesome, glad to help!

[@Viral_Streamerr_Clips]

Thanks Man U saved my exam , god bless you

[@WrathofMath]

Glad to help, thanks for watching!

[@chazy7729]

Thanks for the video.
Amazing video as always. :)

[@WrathofMath]

You're welcome! And thank you :)

[@EtunaHifikepunye]

Very useful🙏🙏

[@hajjex_9086]

You life saver
Thanks for this epic lesson.
Your a legend

[@WrathofMath]

So glad it helped! You’re welcome and thanks a lot for watching!

[@abhisheksinghmajhilia7078]

Thank you! Your video is very helpful. Please make more videos on Alligation and Mixtures.

[@johnyeomans7262]

Is there any way to find the chord length without knowing the angle and only knowing the radius? Please help - I need this for my maths assignment

[@WrathofMath]

Thanks for watching, I am not sure what you mean! Certainly if we ONLY know the radius, we cannot know the length of the chord because we would know nothing at all about the chord, aside from it residing in a circle of radius r. For example, in a circle of radius 1/2, a chord could be as big as 1 (if it was a diameter) or any number less than that.

[@kalsept]

banger even after 5 years tnx

[@WrathofMath]

Glad to help!

[@yotypical_girl]

yeah

[@kickboxing3728]

Haha I had two math videos open and both of them (yours and one other) included bird sounds in the background!

[@WrathofMath]

That's a funny coincidence! Thank you for watching! If you watch some of my new lessons, they have real bird sounds because they're out in the woods! ua-cam.com/video/KAw1x_nbERQ/v-deo.html
Or if you like spookier ambience, my Halloween lessons have some of that: ua-cam.com/video/2GeqKVqwPfc/v-deo.html

[@sattwikbiswas4063]

I am from India. Thank you so much sir for this video. My entire concept has been cleared. I have a question for you sir. Suppose in an isosceles triangle if we draw median from any vertex on its opposite side does the median bisect the angle from whose vertex it has been drawn?

[@nangulaitengula]

To find the chord length will we always use sin? Or is it in accordance to angle give, For example we where given the angle at the chord

[@mihirmalladi8494]

You don't have to use sin to find the chord length. I used cos and got the solution of:
2 sqrt((r^2) - ((r cos(theta/2))^2))

[@tshidisopretty3275]

How did you manage to find "70°" ??

[@craigwilson8255]

It was an example, so he gave a random radius and angle. I'm not sure how to find it if we don't already have one of the angles, or "x"? Hope you got it figured out by now though lol.

[@ryanmalapit1516]

What if the only given is the radius how could you solve the teta ø?

[@Emerson_Beau]

Assume it's 90

[@jhngamingytph1079]

This video help me to answer my test and homework thanks for uploading it

[@WrathofMath]

Glad it helped, thanks for watching!

[@abdulnaffay3652]

I’m getting 10.44 for the actual answer how is it 11.18

[@WrathofMath]

Thanks for watching! I'm not sure how you're getting 10.44. The answer is not 11.18, it is 11.48. You could double check your calculator is using degrees, though using radians would not give you 10.44 either.

[@nerdlover]

You are indeed a good teacher

[@WrathofMath]

Thank you!

[@simpleman283]

I learned how to do this w/law of cosines, but this sin rule is awesome.

[@WrathofMath]

Thanks for watching! The sine rule is a real treat!

[@kkww5034]

Why did you assume theta is 70 °

[@buddho1135]

Sad as these great videos go unseen by the bulk of UA-cam audience are maximum are looking for pole dancers

[@StennettaFleming]

Thanks for the lesson .

[@anthonycasarella2000]

Thanks

[@WrathofMath]

Thank you for watching! Let me know if you ever have any requests!

[@machinedoctor3917]

Thanx amazing

[@WrathofMath]

Thank you for watching!

[@fjejejjrbskjwjw163]

THANKS YOU

[@WrathofMath]

YOU'RE WELCOME!

[@richardrutebeka6109]

Thanks for the good information🙏🙏🙏🙏🙏

[@lasithaaththanayake]

Thank you

[@WrathofMath]

My pleasure!

[@amealiarichards3471]

@@WrathofMath hey I got 11.47cm on my end would it still be correct ?

[@rajkumarrajkumar-wo1zo]

Thank you so much

[@Jokerboy152]

Thank you so much brother... Really informative

[@WrathofMath]

My pleasure, thanks for watching and let me know if you ever have any questions!

[@brd8764]

A chord is a finite line segment. It is a measurable length of line.

[@manicmath3557]

Do you use ipad or pc. Wat programme do u use. I wanna try my own cideos and your rpgramme seems perfecr. Could yoy tell me. Thank you

[@joshuatobi2109]

Well explained

[@WrathofMath]

Thank you!

[@ahmedmiraan4682]

isn't X half the chord length because we basically bisected the triangle to make it a right angled triangle ?

[@shantanudingole5155]

How to solve when theta is not given

[@JosephElfassi]

Great stuff!

[@WrathofMath]

Thanks Joseph! Let me know if you ever have any video requests!

[@gifworld4256]

Hey

[@isaaccasarez4299]

Man I’m getting 11.97 😅 helppppp please.

[@richardowens6843]

Why not use law of cosines?

[@dorcasnhyira4593]

You are too much😘. God bless you

[@WrathofMath]

Thank you for watching! If you're in the mood for some tunes, check out my new math song that came out today! 😊 ua-cam.com/video/0Oro28Xkzbg/v-deo.html

[@tristanpatterson8375]

this should be 3 min long

[@WrathofMath]

ua-cam.com/video/o5DjN3fzim4/v-deo.html

[@GodJesusChristlovesyou_knows_u]

Brothers and Sisters, God loves us so much that He sent His Son Jesus Christ for us to save us from our sins, and he bled and died on a cross for us to redeem us from death, and to gain life everlasting, for those who put their trust in him. And what's more, he has risen, and is willing to call you to repentance (correction) and as his witness, by his grace indeed. "For it is by grace you are saved, through faith". Jesus loves you, God cares for you! Therefore, repent and believe the gospel.

[@Studiesfortopper]

Amen !!! I receive it Jesus Name

[@Studiesfortopper]

Every one , spread the gospel before it is too late

[@Studiesfortopper]

GOD Bless All❣️

[@JesusChristlovesyou_friend]

@@Studiesfortopper ❤❤

[@ammarsaada9923]

That’s a lie

[@gifworld4256]

Remember me!
It's been a long time!

[@chazy7729]

He is a best teacher. :)

[@WrathofMath]

Yes of course! Days go by quickly for me, it doesn't seem long at all! Did you see my response to your request for a lesson on area? I just wanted a few more details on what you're looking for. Let me paste my response here, for your convenience. I said...
Sure! What kind of lesson are you thinking? Do you want to know how to find the area of a specific shape, or do you have something else in mind?

[@shahadattalukder9226]

the background birds sound is annoying . I hate to say, however I like natural birds sound

[@WrathofMath]

Sorry to hear you found it annoying! The vast majority of my lessons have no background noise, but on occasion I include some for seasonal lessons and the like. Let me know if you ever have any questions!

[@kalsept]

w guy

[@elimartin5105]

Never seen someone say so much uses stuff in my life

[@Parveshkumar-tj2fj]

You are so cute❤

[@Ankitkumar-nf8ix]

Kya bak raha hai

[@yotypical_girl]

this vdi i sreally help ful but i just wanted to let you kno wthat it is 11.47 not 48 because if we round 11. 47152873 it becomes 11.47

[@rajuthoppil3393]

Thanks

[@WrathofMath]

No problem!