Can you find the area of the yellow circle? | (Three circles) |

Learn how to find the area of the yellow circle. Area of the blue and green circle are given as 144pi and 256pi. Important Geometry skills are also explained: Circle theorem; area of the circle formula; Pythagorean Theorem. Step-by-step tutorial by PreMath.com
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Step-by-step tutorial by PreMath.com
• Can you find the area ...
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Can you find the area of the yellow circle? | (Three circles) | #math #maths
Olympiad Mathematical Question! | Learn Tips how to solve Olympiad Question without hassle and anxiety!
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[@abeonthehill166]

Man your examples are so clear and step by step easy to follow ; you make Maths great fun ! …..Thanks for sharing. ……Abe ( uk )

[@PreMath]

Glad you like them! Thanks ❤️🌹

[@misterenter-iz7rz]

A trapezoid forms inside three circles with sides r,24,16,16+r, where two radii are parallel, thus 24^2+(16-r)^2=(16+r)^2, 64r=576, r=9 therefore the answer is 81pi.😊

[@santiagoarosam430]

Llamaremos T al punto de tangencia verde amarillo》AOB es rectángulo y semejante a ATO y a OTB》AT=16=4×4 y OT=12=4×3》AO=4×5=20》OTB también es triángulo 3/4/5》OT=12=3×4》TB=3×3=9》Área amarilla =81Pi Gracias y saludos.

[@notovny]

For me, it was realizing that ADO and BCO were similar right triangles (each half of corresponding similar right-angled kites), and recognizing the Pythagorean Multiple of the 3-4-5 triangle in ADO.

[@HappyFamilyOnline]

Very well explained 👍 Thanks for sharing

[@DR-kz9li]

r/12=12/16 ; 16r=144 r; r=9 Thanks for the lesson. Excellent way of teaching. My last math lesson : 1971. I've been following your lessons for one year and half. I'm learning....

[@robertbourke7935]

A nice exercise

[@ybodoN]

Another method: △ADO and △BCO are each the half of a right kite ⇒ △AOB is a right triangle similar to △ADO and △BCO. Therefore AB = 20² / 16 = 25 and the radius of the yellow circle is 25 − 16 = 9 cm so its area is 81π cm².

[@Okkk517]

A simple and short solution.

[@yalchingedikgedik8007]

Thanks Sir Very nice and useful exercise With my glades .

[@mathbynisharsir5586]

Excellent explanation sir 👍

[@ybodoN]

Generalized: the radius of the yellow circle is *_b²/a_* where *_a_* is the radius of the green circle and *_b_* is the radius of the blue circle.

[@soli9mana-soli4953]

On the green and white circles AO is 20 with Pythagorean th. Notice that 20 is AD + DO - 2*(AD - DO) = 16+12 - 2*(16-12) = 28 - 8 = 20 so, simmetrically, I did the same with the yellow and the white circles... OB = OC + BC - 2*(OC - BC) = 12 + r - 24 + 2r = 3r - 12 then applying Pythagorean th. on OBC (3r - 12)² = 12² + r² r = 9

[@quigonkenny]

Green circle: A = πr² 256π = πr² r² = 256 = 16² r = 16 Clear circle: A = πr² 144π = πr² r² = 144 = 12² r = 12 Let O be a point where CO is parallel with AD and perpendicular to DC and passes through B, and AO is parallel to DC and perpendicular to AD. By observation, AO is congruent with DC, AB is equal in length to the sum of the green circle radius 16 and the yellow circle radius x, and OB is equal in length to the difference between the green and yellow radii. By Pythagorean Theorem: a² + b² = c³ OB² + AO² = AB² (16-x)² + (24)² = (16+x)² 256 - 32x + x² + 576 = 256 + 32x + x² -32x - 32x = -576 64x = 576 x = 9 Yellow circle: A = πr² = π(9²) = 81π cm²

[@prossvay8744]

256π=πR^2 R=√256=16cm 144π=πr^2 r=12cm 24^2+(16-x)^2=(16+x)^2 x=9cm area of the yellow circle=81πcm^2 Thanks❤❤❤

[@bigm383]

Great work, Professor!❤

[@PreMath]

Thank you! Cheers! ❤️

[@normanc918]

Thank you sir. I only worked up to the points of AD =16, DC =24. I had no idea to do the rest, until I watched your explanation.

[@raya.pawley3563]

Thank you

[@Ibrahimfamilyvlog2097l]

Great work sar❤❤❤❤❤❤

[@PreMath]

So nice of you ❤️

[@wackojacko3962]

More fun! 🙂

[@Copernicusfreud]

Yay! I solved the problem.

[@uditproyt5486]

Solve: sin^8x-cos^8x/(2-cos²x) (sinx+cosx)

[@kiratsinghsaluja9123]

81pi 24^2+(16-r)^2=(16+r)^2

[@jeremykomlabekui3311]

Trigonometry ratios can be used

[@AmirgabYT2185]

S=81π≈254,34

[@B715]

Does this solution only apply if you assume that the line EB is equal to the diameter of the blue circle, which you can not do unless you assume that the drawing is true to scale?

[@giuseppemalaguti435]

(16+r)^2=24^2+(16-r)^2...r=9

[@dotsucks]

Im so sad i got the logic right but forgot to double the r=12 value in the final calculation :(

[@Alishbafamilyvlogs-bm4ip]

New subscriber like Dan❤❤ very nice video

[@PreMath]

Thanks for subbing!🌹

[@laxmikatta1774]

Day 11 but I won't comment because sir has given a guarantee 😊😊