Calculate area of Yellow shaded region | Radius of the big circle is 12 | Important skills explained

Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!

Need help with solving this Math Olympiad Question? You're in the right place!

I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at

Calculate area of Yellow shaded region | Radius of the big circle is 12 | Important skills explained

Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!

#CalculateAreaOfYellowShadedRegion #CalculateArea #AreaOfCircle #PythagoreanTheorem #AreaOfTriangle#GeometryMath #CircleTheorem #PerpendicularBisectorTheorem
#MathOlympiad #ThalesTheorem #RightTriangle #RightTriangles #CongruentTriangles
#OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths #MathOlympiad #HarvardAdmissionQuestion
#MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #CollegeEntranceExam
#blackpenredpen #MathOlympiadTraining #Olympiad Question #GeometrySkills #GeometryFormulas #Angles #Height
#MathematicalOlympiad #OlympiadMathematics #CompetitiveExams #CompetitiveExam

How to solve Olympiad Mathematical Question
How to prepare for Math Olympiad
How to Solve Olympiad Question
How to Solve international math olympiad questions
international math olympiad questions and solutions
international math olympiad questions and answers
olympiad mathematics competition
blackpenredpen
math olympics
olympiad exam
olympiad exam sample papers
math olympiad sample questions
math olympiada
British Math Olympiad
olympics math
olympics mathematics
olympics math activities
olympics math competition
Math Olympiad Training
How to win the International Math Olympiad | Po-Shen Loh and Lex Fridman
Po-Shen Loh and Lex Fridman
Number Theory
There is a ridiculously easy way to solve this Olympiad qualifier problem
This U.S. Olympiad Coach Has a Unique Approach to Math
The Map of Mathematics
mathcounts
math at work
Pre Math
Olympiad Mathematics
Two Methods to Solve System of Exponential of Equations
Olympiad Question
Find Area of the Shaded Triangle in a Rectangle
Geometry
Geometry math
Geometry skills
Right triangles
imo
Competitive Exams
Competitive Exam
Calculate the Radius
Semicircle
Pythagorean Theorem
Circle Theorem
Right triangles
Perpendicular Bisector Theorem
Square
Area of triangle
Area of circle

Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

[neelaramramesh]

Thank you 🙏🙏 professor wishes from Bharat

[alster]

After the Pythagorean Theorem, the problem became easy and paused the video and solved it on my own.

[misterenter-izrz]

Generally, if R is the radius of the big circle, the radius of the smallest circle is R/3, thus the area is (R^2 pi=7/18 R^2 pi.

[spiderjump]

Radius of blue circles = 12/2=6
Let r be radius of smallest circle .
(6+r)^2= 6•6 + (12–r)^2
36+12r+r^2=36+144–24r+r^2
36r=144
r=4
Yellow area =pi144–pi16-pi36•2
= 56pi

[Copernicusfreud]

Yay! I solved it, 56*(pi). The hardest part for me was calculating the r value for the green circle at 4 units. I did not have a pencil or paper or calculator, but I was able to do it. I was lucky that r^2 and 36 were on both sides of the equation to cancel out with the math.

[santiagoarosam]

R=12 → Radio azul =a=R/2 =6 → Si radio verde =b; en el triángulo BAD: (a+b)²=a²+(12-b)² → b=12/3=4 → Area amarilla = Pi(12² - 2x6² - 4²) =56Pi =175.93
Gracias y un saludo.

[misterenter-izrz]

Suffice to determine the radius r of green circle, by pythagorean theorem, 6^2+(12-r)^2=(6+r)^2, 36+144-24r+r^2=36+12r+r^2, then 36r=144, r=4, therefore the area is 12^2 pi-2x 6^2 pi-4^2 pi=(144-72-16)pi=56pi=173.93 approximately. 😃

[vara]

👍Prof, a great problem and a wonderful solution. Looking forward to viewing such interesting problems.

[zawatsky]

Не помнил точно про центры, пока не увидел. Теперь всё сходится.

[vidyadharjoshi]

AD = 12 - r. AB = 6 + r. ABsq = BDsq + ADsq. r = 4. Area = 144pi - 2*36pi - 16pi = 175.93

[TonTin]

The area of yellow region is 56π, thank you for teaching me PreMath. (My real name is Andreu)

[theoyanto]

I love these, but I always struggle to begin, but once I see you first moves, I understand, so I need more like this one please, it's quite annoying, I can see my error, I guess I don't fully understand the methodology yet, hey ho, more practice, needed
I think the idea is to represent the unknown in a way that doesn't introduce another variable, I see it, but maybe I get it one day thanks again 🤓👍🏻

[wackojacko]

This problem I feel is like the Hunt for Neptune's Gold...and in this case we found it. cool!🙂

[DeltaMikeTorrevieja]

Question: why keep the pi in the results so late. If i know something is 16pi I'm multiplying 16 * 3.1415 as early as I can. Why do you keep them in right up to the end?

Asking for myself, I have no friends (obviously, I watch maths videos on YouTube)

[martinbrederoo]

I took a different approach and came to a different conclusion. Where do I go wrong? Thanks in advance. I took the trangle ABC. AB and AC are 6+r, BC = 12. Thus, (6+r)^2 + (6+r)^2 = 144 -> r^2 + 12r + 36 + r^2 + 12r + 36 = 144 -> 2r^2 + 24r + 72 = 144 -> r^2 + 12r - 36 = 0; r = (-12 +/- sqrt(144 - 4*1*-36))/2*1 -> r = (-12 +/- sqrt(288))/2 -> r = 2.485, which leads to a yellow area of ca 206.8.

[misterenter-izrz]

How to solve this generally r=R/3, where r, R are radii of small and large circles without using pythagorean theorem?

[srinivasansundararajan]

If ck is common tangent to A and B then ck^2=12^2-6^2=108. So 108+r^2=(6+r)^2 resulting in r=6. Sir can you explain where I made a mistake?TIA

[ybodoN]

Amazingly, this construction produces 3:4:5 right triangles...

[francismoles]

We can sauy that the area of the yellow region is equal of 176 square units because pi is also equal at 22/7

[hamidaqayyum]

[]《 *_Absolutely Beautiful Presentation and sharing_* 》 []
[]《 *_Greetings and Blessings from Hamida Qayyum_* 》 [] LIKE 384