At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Hey! We 've verified this expert answer for you, click below to unlock the details :)

SOLVED

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

anonymous

A regular polygon, with 49 sides, is inscribed in a circle. How many triangles with vertices that are vertices of the polygon have the centre of the circle in their interior?

Not the answer you are looking for? Search for more explanations.

More answers

asnaseer

For an 'n' sided polygon, if we label each vertex of the polygon from 1 to n and consider the triangle from the center of the circle to the first two vertices, we get this diagram:
|dw:1324760887506:dw|
Now consider some vertex labelled 'i'. We need to pick the position of this vertex such that it lies between the projections of vertex 1 and 2 through the center of the triangle - this will ensure that a triangle drawn between vertices 1, 2 and 'i' will contain the center of the circle.
This leads us to this inequality:\[
\begin{align}
\pi+\frac{2\pi}{n}&>&\frac{2\pi}{n}*(i-1)&>\pi\\
\therefore n+2&>&2(i-1)&>n\\
\therefore \frac{n+2}{2}&>&i-1&>\frac{n}{2}\\
\therefore \frac{n+4}{2}&>&i&>\frac{n+2}{2}
\end{align}\]so, for a polygon with 49 sides we get:\[26.5>i>25.5\]and since 'i' has to be an integer, there is only only one solution which is \(i=26\). So for the edge between vertices 1 and 2, we can construct just one triangle to vertex 26 which contains the center of the circle. Since this polygon has 49 edges, we can therefore form 49 such triangles.
So I think the answer is 49.

anonymous

i think i have got the solution to this,
it comes out to be a series,
for a polygon with n sides,
if n is odd then ans is n-1/2
for even n
ans is n-4/2
i got that by anlysing the cases of hexagon, septagon and octagon, and seeing the pattern