# Solution 72: Hexagon Inside a Nine-Point Circle

Embed

**Published on Dec 27, 2018**- Let's use a property of the Nine-Point Circle to compare the areas of an inscribed hexagon and the triangle.

Congratulations to attyfarbuckle, Luis Perez, Eric Schneider, Farzad Saeidi, Devansh Sehta, and Henry M. for successfully solving this math challenge question! attyfarbuckle was the first person to solve the question.

Your support is truly a huge encouragement.

Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos!

Every subscriber and every like are wholeheartedly appreciated.

For more Weekly Math Challenges:

usclip.net/p/PLpoKXj-PWCbaDXYHES37_zX4O-kCWxguM

Certainly NOT the best pianist, but still4 months agoME: *reads the riddle*

ME: I bet, that the hexagon's area will be half the triangle's area!

ME: *watching video*

ME:

ME: Indeed

I watched too many mathematic riddles not to expect a ridiculously simple ratio ;)

Rahul5 months agoOn the real line place an object at 1.After every flip of a fair coin ,move the object to the right by 1unit if the outcome is head and to the left by 1 unit if the outcome is tail. Let N b a fixed positive integer .Game ends when the object reaches either 0 or N . Let P(N) denote the probability of the object reaching N.Find the formula for P(N) for any positive integer N.

Rahul5 months agoIn the complex plane ,let u,v be two distinct solutions of z^2019 -1=0. Find the probability that |u+v|>_ 1 .

Rahul5 months agoSolve this please

Find all polynomials p(x) such that (p(x))^2 = 1+ xp(1+x) for all real numbers x

Lewis Tran5 months agoI'm loving these videos, even as a non-mathematics major. What hardware and software do you use for your videos?

Omar Fahmy5 months agoCan anyone help me in this problem : "find with proof all prime p and q for which p

^3 + 19q^3 + 2018 is the cube of a prime" ?

Radhika Shenoy5 months agoWow you are intelligent in solving difficult maths problem.

Himansh Negi5 months ago^{+1}I have a tip for you,

Just start solving IIT-Jee integration problems and get flooded with views and subscribers.

Thank me later. You deserve more subs.❤️

adandap5 months ago^{+9}Having never laid ears on the nine-pint circle before, this problem was hard work. I ended up just brute forcing it with coordinate geometry. Thankfully Mathematica looked after the tedious algebra.

Felipe Lorenzzon5 months agoI didn't post a solution because I was late. I did it by connecting the points shown on the circle to its center and finding all angles by using parallel lines and triangle similarities. Then, trigonometry gave me the length of every segment and I found the area. A bunch of work

Sudheer Thunga5 months agoWe could also use the properties of the altitude being dropped on the side(a=bcosC+ccosB) to get it directly.......

UbuntuLinux5 months ago^{+2}Extra: CIB is a 30-60-90 triangle, so BC = 2BI. D is mid of BC so BD = 1/2BC = BI. Triangle BID has a 60° angle and two equal/congurent(?) side, so it's equiterial

Arbitrary Renaissance5 months agoHoly cow. Yeah, I wasn't going to get this one. xD

Gergő Dénes5 months agoOur teacher talked about the Euler-line and the Nine-point Circle (In our language it's mentioned as Feuerbach-circle), but she only showed us the proof for the Euler-line :/

Overall great video, and shows how much impact knowing a small fact can have.

an–bn5 months ago❤️

Johannes H5 months agoGood thing I didn't try that one

Or maybe not, but I don't know many geometric tricks

James Wilson5 months ago^{+5}Very cool! That is yet another interesting thing you can do to a triangle! I may have never known that had I not watched this video.

Alexander Mendez5 months ago^{+1}I would have used analytic geometry, but your solution is easier.

Andrés Robles5 months agoDonde puedo ver esos challenge?

Anto155 months agousclip.net/video/YN9Keh2HSSg/video.html