Can You Find X in this Geometric Shape? | Step-by-Step Tutorial
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- Опубликовано: 20 фев 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 Хобби
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
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.
you are great sir.......what a way of explanation to such an
incredible problem
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Nice. Very good indeed.
Solved it in a similar way, just by using sum of angles in triangle and straight line.
I like the problem explanation very much
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sure can, thanks for the challenge bro
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Excellent sir!!!!
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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)
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Great
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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👍👍👍👍more geometry problem please and thanks!
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V nice circle question with exterior angle playing an important role
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\
Extremely beautiful sir
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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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amazing video, I watch this video with full concentration
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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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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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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. :)
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:
How do you know that ABO is isosceles triangle??
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
wow!!
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Very nice geometry question!!! My exams are there so I will not be able to check up your videos
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I.have been watching your videos for six months
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nice
Super
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Yes...i am able to do this...😊
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@@PreMath Thank you sir😊❤️
66 degrees. Good question it was.
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I had no idea abt exterior opposite angle theorem
Solved easily
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Great Great Great
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Wow
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Hmm, I didn't catch that AB = OC.
No worries. We are all lifelong learners.
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Suport from me
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70.... Anzi 66
Easy
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
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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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
😁"Isosceles triangle " is the key point!! Fantastic solution!!
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