Can you solve for X and Y? | Two semicircles in a rectangle | (Math skills explained) |

[@misterenter-iz7rz]

First like adder。🎉

[@PreMath]

Excellent! Thank you! Cheers! 😀 You are awesome. Keep it up 👍

[@marioalb9726]

y = R Tangent secant theorem: (x -R)² = 7. (7+11) (x - y)² = 126 x = y + √126 Pytagorean theorem: x² + y² = (7+11)² (y + √126)² + y² = 18² y² + 2.√126.y+126 + y² =324 2y² + 2.√126.y -198 = 0 y² + √126.y -99 = 0 y = 5,811 cm x = 17,036 cm ( Solved √ )

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@parthtomar6987]

Nice solution sir

[@PreMath]

Thanks and welcome You are awesome. Keep it up 👍

[@JSSTyger]

You do outstanding work. This one had me stumped.

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀 You are the best. Keep it up 👍

[@Aryan_1Official]

Best explanation

[@PreMath]

Glad you think so! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@JLvatron]

Wow, brilliant!

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@chelliahRaveedrarajah]

Very interesting question sir.

[@PreMath]

Many many thanks You are awesome. Keep it up 👍

[@ybodoN]

Once we have xy = 99 and x² + y² = 324, we can set the quadratic equation x⁴ − 324x² + 9801 = 0. Since we would get the same equation with y, the positive solutions 3 √(18 ± √203) are x and y. These can be denested to obtain x = 3/2 (√58 + √14) and y = 3/2 (√58 − √14) in their exact form. PreMaths' amazing solution avoids both the quadratic equation and the denesting operation! 🤩

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@tombufford136]

At a quick glance, Important to note the lines AP and PC are chords of circles and not the diameters.

[@Abby-hi4sf]

Beautiful!

[@PreMath]

Thank you! Cheers! You are awesome. Keep it up 👍

[@soli9mana-soli4953]

An alternative solution can be found with tangent secant theorem. Called OH the perpendicular to BC from the center of the bigger circle, we can write: AC : CH = CH : CP 18 : CH = CH : 7 CH = √ 126 Now applying Pythagorean theorem on ABC right triangle we get: y² + (y+ √ 126)² = 18² y² + √ 126y - 99 = 0 then y = (√ 522 - √ 126)/2 x = (√ 522 - √ 126)/2 + √ 126) = (√ 522 + √ 126)/2

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@waheisel]

Nice! Math is so cool that there are different proof for us to discover. As usual PreMath's solution was more elegant and clever than mine (I brute forced it with a lot of algebra including denesting radicals and rationalizing the denominators).. Your solution is even more concise!

[@soli9mana-soli4953]

@@waheisel thank you

[@toontime1415]

Sir, you are a good teacher for us to teach Mathematics. Thank you sir. Our greetings to achieve sir.🎉🎉🎉

[@PreMath]

Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@wackojacko3962]

@ 1:06 Thales Theorem is a special case of Euclid's Inscribed Angle Theorem. And of course we immediately engage Pythagorean. Soooooooo cool! 🙂

[@PreMath]

Spot on! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@wackojacko3962]

@ 5:20 Adding 2xy too equation 2...absolutely ingenious! @ 6:50 , same thing! @ 9:44 , most ingenious! 🙂

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@markkinnard796]

Excellent!

[@mohabatkhanmalak1161]

Wow! I am amazed how you solved it teacher. I was thinking of using Trigonometry, but I kept watching the clip and it is wonderful how you got the answers. Thanks for posting.✨

[@HappyFamilyOnline]

Amazing 👍 Thanks for sharing 😊

[@PreMath]

Thank you! Cheers! You are awesome. Keep it up 👍

[@bigm383]

❤👍😀

[@PreMath]

Thank you! Cheers! 😀 You are awesome. Keep it up 👍

[@soniamariadasilveira7003]

A Very hard question Sir

[@PreMath]

Yes! It's a challenging one! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@shreyanshjain2034]

Sir please tell proof of ceva's theorem and menelau theorem

[@PreMath]

Please give me time to do my homework. These proofs are little challenging. Cheers

[@charlesbromberick4247]

It´s not clear to me why the diagonal passes through the point of tangency, but I believe it.

[@maturaczynicuda]

Beautiful

[@PreMath]

Thank you! Cheers! You are awesome. Keep it up 👍

[@DDX01]

Very nice but in the last we should put the x value in eq. 01 xy=99 17.04*y=99 y=99/17.04 y=5.81...... easy way

[@jose-madelsaladorodriguezd3461]

¿CÓMOPUEDO YO PUBLICAR UN PROBLEMA EN ESTA PÁGINA? ESPERO RESPUESTA

[@PreMath]

Enviar el email a: [e-mail] Gracias

[@misterenter-iz7rz]

cos u=x/18=2y/11, y=11x/36, then (1+(11/36)^2)x^2=18^2, x^2=18^2 1296/1417=296.333, x=17.214328 approximately, y=11x/36=5.259934 approximately. 😅 Oh, I make a careless mistake.😅

[@PreMath]

Thanks for sharing! Cheers! You are awesome. Keep it up 👍

[@wackojacko3962]

Comment for yesterday's Menelaus problem. Cevians! They're everywhere! All Hail Giovanni Ceva! 🙂

[@PreMath]

Excellent! Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@arnavkange1487]

Very hard sum

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@giuseppemalaguti435]

x°2+y°2=324...x^2=162+√(162^2-99^2)=290,.....mah,i conti non sono interi...ho dei dubbi

[@PreMath]

Thanks for your feedback! Cheers! 😀 You are awesome. Keep it up 👍

[@giuseppemalaguti435]

​@@PreMath...hai scritto 17.04...allora il mio risultato è ok!!!!

[@padraiggluck2980]

Professor, your source of problems appears to be inexhaustible ❗️