Optimizing Largest Trapezoid in Semicircle Radius a

[ptolema]

Homework Statement

Find the trapezoid of largest area that can be inscribed in a semicircle of radius a, with one base lying along the diameter.

Homework Equations

diameter = 2a
area of a semicircle = (1/2)πr²
area of a trapezoid = (1/2)(b₁ + b₂)h

The Attempt at a Solution

so i know that one of the bases is the diameter 2a, and that i need to maximise the area of the trapezoid. the length of the second base is anywhere between 0 and 2a, and the height is between 0 and a. that being said, i find myself working with too many variables in the trapezoid area equation. i don't know how to reduce the number of variables i have and relate the trapezoid formula to the semicircle formula. as far as i can tell, the semicircle's area (and circumference) is a constant, so it doesn't do much good in eliminating variables. where do i even begin to make sense of this?



here's another:

Homework Statement

A right angle is moved along the diameter of a circle of radius a (see diagram). What is the greatest possible length (A+B) intercepted on it by the circle.

[PLAIN]http://www.esnips.com/nsdoc/207fd3b5-1a2f-460f-b911-3b3eda3a7c2a

Homework Equations

so, the pythagorean theorem might be useful
diameter = 2a

The Attempt at a Solution

this one is even more confusing than the first. i have to maximise A+B, but i don't exactly have an equation to do that. maybe maximising A²+B² would work, but that still leaves me with too many variables. i don't know how to relate anything from the circle to the right angle besides the obvious diameter. i know that 0<A<a and 0<B<2a, but this once again gets me nowhere. no idea where to start, please help!

 

[fzero]

Relate the height and 2nd base of the trapezoid to the point (x.y) where the corner intersects the semicircle. (x,y) is constrained by the equation of the circle (not the area, the geometric equation defining the circle).