Question

http://i158.photobucket.com/albums/t120/brinazarski2/photo-7.jpg

In the figure above, OX is a radius of the circle with center O. Which of the following triangles has the least area?

A AOX
B BOX
C COX
D DOX
E EOX

I know the answer is A... but why?

Answer 1

\[ \because r is constant ,\therefore r ^{2} is also constant , hence area depends on \sin \theta only\]
maximum value of sin theta is 1 and is attained only at theta=90
as the value of theta increases or decreases from 90 its value decreases
\[\because \sin \left( 180-\theta \right)=\sin \theta \]
so A is right choice angle is nearly 180 may be 170 or165 etc.,