geometry

This topic has expert replies
Senior | Next Rank: 100 Posts
Posts: 41
Joined: Wed May 30, 2012 5:21 am
Thanked: 3 times

geometry

by shrutib » Wed May 30, 2012 7:18 am
What is the greatest possible triangular region with one vertex at the center of a circle of radius 1 and other two vertices on the circle?

Answer-1/2

User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Mon Apr 16, 2012 8:40 am
Location: Pune, India
Thanked: 186 times
Followed by:29 members

by aneesh.kg » Wed May 30, 2012 8:09 am
shrutib wrote:What is the greatest possible triangular region with one vertex at the center of a circle of radius 1 and other two vertices on the circle?

Answer-1/2
I had to use a little bit of trignometry to prove that the area will be maximum when the angle = 45.

Image
Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

User avatar
Master | Next Rank: 500 Posts
Posts: 287
Joined: Fri Mar 23, 2012 12:33 am
Location: Pune,India
Thanked: 60 times
Followed by:6 members

by GMAT Kolaveri » Wed May 30, 2012 8:59 am
shrutib wrote:What is the greatest possible triangular region with one vertex at the center of a circle of radius 1 and other two vertices on the circle?

Answer-1/2

Image
Regards and Thanks,
Vinoth@GMAT Kolaveri
https://www.facebook.com/GmatKolaveri
https://gmatkolaveri.tumblr.com/

Click the thank you button if you like my reply :)

Master | Next Rank: 500 Posts
Posts: 215
Joined: Sat Jun 14, 2008 4:24 pm
Thanked: 13 times
Followed by:1 members

by 1947 » Wed May 30, 2012 9:34 am
Though not a proof ...but I read some where to think of clock while doing this question. When the 2 hands of clock are at 90 degrees then the area formed by these hands will be max...

when we increase/decrease this angle the area decreases.
this is just a concept but it explains this.
If my post helped you- let me know by pushing the thanks button. Thanks