Can You Find X in this Geometric Shape? | Step-by-Step Tutorial
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- čas přidán 20. 02. 2022
- Learn how to find the angle in this complex shape made up of a triangle and a circle. Use the exterior angle theorem! Fast and easy explanation by PreMath.com
#OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam - Jak na to + styl
I like of sir.We thank you for all
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I solved it using the property of the exterior angle of a circumference (not of a triangle), for which I also had to draw the segment OB: 22º=(x-22º)/2; then x=66º. Thanks!
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Amazing way of teaching👍
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You are always the best thinks a lot for your helps
you are great sir.......what a way of explanation to such an
incredible problem
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Awesome! I'm thinking the two premises needed to form a conclusion here are: Exterior Angle Thm and Isosceles angle relationship. Thank you for reinforcing critical thinking. 🙂
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@@PreMath I guessed that the initial diagram having (2 identical sides) would give the next 2 angles. I like the way U did it better.
Nice. Very good indeed.
Solved it in a similar way, just by using sum of angles in triangle and straight line.
I didn't know the "Exterior Angle Theorem". However, it makes sense, of course, and the solving of the problem a bit shorter since you don't have to find the missing angles of all the triangles. :)
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I like the problem explanation very much
angle x = angle OAC + angle ACO
= angle OAC + angle CBO
( since ∆ BOC is isosceles, OB= OC)
= 2 angle OAC + angle ABO
= 3 angle OAC = 66°
( since ∆ ABO is isosceles,
as AB= OC = OB)
triangle ABO: angles in pts. A and O = 22°, angle in pt. B = 136°. Then in triangle BCO: angles in pts. B and C = 44° and angle in O = 92°. Thus x = 180° - 92° - 22° = 66°
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I solved it drawing a specular triangle to A0C. Some minutes lost, anyway I 'm happy of my progress in math. Thanks for your lessons: 3 months ago I didn' t know what an exterior angle was!
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another approach using intersecting secant properties.
Let AO cut the circle at D and E forming two sectors on circle arc BD...smaller and arcCE ... Larger
the property is angle OAC = 1/2 (Larger arc- Smaller arc) ; 1/2(arcCE-arcBD)
arc CE = x and arc BD = 22 ( you arrived at) also OAC = 22 given
therfore angle OAC 22 = 1/2(x-22)
x - 22 = 44
x = 66
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V nice circle question with exterior angle playing an important role
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\
👍👍👍👍more geometry problem please and thanks!
More to come!
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amazing video, I watch this video with full concentration
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sure can, thanks for the challenge bro
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X = 66 degrees. ABO is an isosceles triangle (OC is the Radiusses is thus also OB). The angle OBC is 44 (exterior angle theorem), which renders the angle BOC as 180-44-44=92. Thus x is 180-92-22=66.
I did the same
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Join OB. Now AB=OC=OB.
So Angle OBC=AngleOCB=2×22= 44 degrees.
So the required angle x=44+22= 66 degrees.
I got 66 degrees but by a different route:
Sum of 345 is 12
But here is 216 that is 12×18
Multiplier is 18
3×18=54
4×18 =72
5×18=90
Mukundsir
Extremely beautiful sir
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How do you know that ABO is isosceles triangle??
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Nice Thanks🌹🌹🌹
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Very nice geometry question!!! My exams are there so I will not be able to check up your videos
Best of luck on your exams
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I.have been watching your videos for six months
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I had no idea abt exterior opposite angle theorem
wow!!
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nice
Super
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66 degrees. Good question it was.
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😁"Isosceles triangle " is the key point!! Fantastic solution!!
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Solved easily
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Yes...i am able to do this...😊
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@@PreMath Thank you sir😊❤️
Great Great Great
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Wow
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Couldn't solve it just by looking at the thumbnail because the thumbnail doesn't show those two line segments being of equal length. lol
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70.... Anzi 66
Easy
Hmm, I didn't catch that AB = OC.
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Approve
LOL The thumbnail omitted AB=OC! I tried to solve it before starting the video and wasted 10 minutes breaking my brain over how the damn thing could ever be solved. xD
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1/2x=22
X=44
It is easy to prove that x is the triple of the first angle !
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no more 1 min, X = 66
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66
Great
Super duper easy ans: x = 66 degree
The answer is x = 66 degree lol
Cross check my friend
@@Teamstudy4595 yes ans is x=66 degree but if line ac would have touched the outer side of circle then it would've x=44 degree