Points A and B lie on a circle, centre O, radius 5 cm. Find the value of angle AOB that produces a maximum area for the triangle AOB.
This is my work and attempt:
So I will describe my diagram. It is a circle, with a triangle inside (not right angled) in the middle of the circle is a dot labelled O. From here I randomly drew point A and point B, on the edge of the circle and then connected points AOB to form a triangle in the circle. Side OB will be labelled 5 cm as well as AO for radius.
Then in the middle of AB i chopped it in half and drew a line down the middle to point O to form two right angled triangles.
Now I can begin:
Max area of triangle
A=0.5 b h
=(0.5) 5cosx (5sinx)
A'=0 when x=pi/4
But this is only half of theta or angle O, so times two.
pi/4 x 2
Now this answer is correct with the back of the book BUT It doesn't work so well because when i plug it back into my area formula, it turns out the angle is 0.. which cannot be max?
So my area formula must be wrong.
What is wrong from my work and how do i fix it? demonstrate.