WHAT IS THE CIRCUMFERENCE OF THE CIRCLE?

[@PS-mh8ts]

You can also solve it like this, using Stewart's theorem. With points labeled as in the video, we apply Stewart's theorem to △BEC. BO is the median from vertex B to side EC. Stewart's theorem gives the length of the median as follows: 2BO=√(2BE²+2BC²-CE²) -- (i) Here, BO=r-1 (letting r be the radius of the circle) BE=11, BC=7, and CE=2r From (i), we get: 2(r-1)=√(2.11²+2.7²-4r²) 2(r-1)=√(242+98-4r²) 2(r-1)=√(340-4r²) Squaring both sides, we get: 4r²-8r+4=340-4r² i.e., 8r²-8r-336=0 or, r²-r-42=0 i.e., (r-7)(r+6)=0 r being positive, we get r=7 Hence the circumference of the circle=2πr=2π.7=14π units

[@satrajitghosh8162]

(r^2 + ( r - 1)^2 - 7 ^2 )/( 2 r ( r - 1)) = (11^2 - r^2 - ( r - 1)^2)/( 2 r ( r - 1)) r^2 + ( r - 1)^2 = (7^2 + 11^2)/2 2 r^2 - 2 r + 1 = 85 r^2 - r - 42 = 0 (r - 7)( r + 6) = 0

[@lasalleman6792]

I couldn't follow this guy's arguments. I just used the formula: p^2 + q^2 = 2(x^2 + y^2) This formula shows the relationship between the sides and diagonals of a parallelogram. Here, Here, p & q are diagonals of parallelogram. And x & y are the adjacent sides of a parallelogram. I did some estimating with the help of the formula. Came up with 14 for diagonal. Not too precise, but might help if you are triying to get the answer quicktime. Many of this guy's explanations are very hard to follow.

[@Center1ForMathematics]

Thanks for your constructive comment. It might be easy for you but it is not easy for many people out there. For this reason, we provide solution starting from the basic to the advanced level (include labelling points, constructing lines and so on). We know that you might have an idea on how to solve the question but not everyone has. So,be patient with us and follow the procedure. The circumference of the circle is not just 14 but 14 pi.