Can you find area of the circle? | (Radius) | #math #maths | #geometry

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

Can you find area of the circle? | (Radius) | #math #maths | #geometry

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

#FindArea #Circle #ThalesTheorem #IntersectingChordsTheorem #Chords #GeometryMath #PythagoreanTheorem #Euclid'sTheorem #EuclideanTheorem
#MathOlympiad #RightTriangle #RightTriangles #ThalesTheorem
#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 #ComplementaryAngles
#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
Andy Math
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 length AB
Pythagorean Theorem
Right triangles
Intersecting Chords Theorem
coolmath
my maths
mathpapa
mymaths
cymath
sumdog
multiplication
ixl math
deltamath
reflex math
math genie
math way
math for fun

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

[marioalb]

(2R-3)•3=9•4
6R= 9•4+9 =45 cm
R = 45/6 = 7, 5 cm
A =πR² = 56, 25π cm² ( Solved √)

[himo]

9*4=3*(2r-3) 36=6r-9 6r=45 r=15/2
Circle area = 15/2*15/2*π = 225π/4

[Waldlaeufer]

Due to the 90° angle (Thales), COD are collinear:
Following the Intersecting Chord Theorem, we can state:
3 (2r - 3) = 9 * 4
6r - 9 = 36
6r = 45
r = 45/6 = 15/2 = 7.5
A(circle) = r²π = 225/4 π = 56.25 π ≈ 176.71 square units

[MrPaulc]

Intersecting chords: 9*4 = 3(2r - 3), and this line alone ought to be sufficient for the calculation.
36 = 6r - 9
45 = 6r
r = 7.5, or 15/2
r^2 = 225/4
Circle area = (225pi)/4 = 56.25*pi, so 56.25*3.1416...
176.715 (rounded) un^2
This turned out to be much simpler than first appeared, but I used a simpler method than the one shown.
Although we both ended up with the same intersecting chords, it was possible to arrive there sooner.

[phungpham]

1/ The three points C, O, and D are collinear so CD is the diameter.
By using chord theorem we have:
CExDE= AExEB
—> (2r-3)x3= 9x4
—> r=15/2
Area = 225/4 x pi sq units😅😅😅

[KevinTheall]

The Chord Theorem may be applied as follows:
[r + (r - 3)] × 3 = 9 × 4
Solving for r gives r = 15/2.
Hence A = Pi × 225/4.

[santiagoarosam]

Potencia de E respecto a la circunferencia =4*9=3(2r-3)---> r=15/2---> Área del círculo = π15²/2² =225π/4.
Gracias y un saludo cordial

[cyruschang]

Since the corner on top is 90°, the other two points on the circle circumference form the diameter
Apply the intersecting chords theorem
3(2r - 3) = 9(4)
2r - 3 = 12
2r = 15 = the diameter length
r = 15/2 = the radius length
Circle area = (225/4)π

[DiegoSimonetti-zcyj]

per risolvere si calcola prima
la misura del raggio col teorema della corda ponendo :
(2 r - 3) × 3 = 9 × 4 e si ha :
r = 15/2
l'area del cerchio è : π(15/2)^2 = π (225/4)

[alexniklas]

Area= π×(15/2)^2= 225π/4
Thanks Sir!😊

[unknownidentity]

Let's find the area:
.
..
...
....


The triangle ACD is a right triangle. Therefore, according to the theorem of Thales we know that CD is the diameter of the circle. Now we can apply the intersecting chords theorem. With R being the radius of the circle we obtain:

AE*BE = CE*DE = (OC + OE)*DE = (OC + OD − DE)*DE = (R + R − DE)*DE = (2*R − DE)*DE
9*4 = (2*R − 3)*3
12 = 2*R − 3
15 = 2*R
⇒ R = 15/2

Now we are able to calculate the area of the circle:

A = πR² = π*(15/2)² = 225π/4

Best regards from Germany

[wackojacko]

Definitely not drawn to scale. OE seems a little short! 😎

[bijeimath]

I triangoli AED e CEB sono simili (3 angoli uguali).
Risulta:
3/4 = 9/(2R - 3)
R = 7.5
Area S del cerchio:
S = pi•7.5^2 = 56.25 pi
😊

[quigonkenny]

As ∠DAC = 90°, then by Thales' Theorem, we know that DC is a diameter of the circle and thus DC = 2r.

By the intersecting chords theorem, we know that BE•EA = DE•EC. As DC = 2r, and DE = 3, then EC = 2r-3.

BE(EA) = DE(EC)
4(9) = 3(2r-3)
36 = 6r - 9
6r = 36 + 9 = 45
r = 45/6 = 15/2

Circle O:
A = πr² = π(15/2)²
[[ A = 225π/4 ≈ 176.71 sq units ]]

[GrBe-ul]

Get back to work and calculate the yellow area, you know that's what we came here to see.

[joeschmo]

Kewl, did it in my head from the thumbnail. 😂
Couldn't remember the name of the "cross-multiplying" thing, just that it existed. Worked! 🧠🧠🧠

[dinendradhar]

Pl. Solve my problem/ divide any circle by drawing one straight line into two parts such that the area of the bigger is double the area of smaller one.By geomeyricalAlzebra or any mathemetical process. But not by angular process like 360 divide 3 at centre/ Thank and more thanks for future after solving/
D.N.DHAR

[messironaldo]

Wrongly read the question as Yellow area and thus calculated as 3sqrt(14)😅

[marcgriselhubert]

Depuis quelques jours j'entends une TRES MAUVAISE traduction en français au lieu de l'original en anglais. C'est extrêmement pénible tellement c'est mal fait.