One math task!

[tiigrike]

I hope the plot is Ok.
OC=2cm
OB=4 cm , those are fist conditions!
Need to know S=?

 

[srmichael]

S? What is S? The area of the trapezoid? It's not clear to me.

 

[tiigrike]

S? What is S? The area of the trapezoid? It's not clear to me.

I don't know how it's english, but google give me it is area or surface or superficies ...maybe some word is more clear for you . i hope you understand .

 

[tiigrike]

This is not an easy problem so I'll give you some hints.

First construct a perpendicular to AB that runs through C. Call the intersection of this perpendicular and line AB point E.

Next assign letters for your variables. This is always a good idea.
So, let h = length of of AD.
Let t = length of DC.
Let x = length of of EB.
Let y = length of CP.
Let z = length of of BP.
Let s = area of trapezoid.
Let r = radius of circle.

Hint 1: h = 2r. Do you see why?

Hint 2: x² + h² = (y + z)². Do you see why?

Hint 3: s = ht + (hx / 2) = h(2t + x)/2. Do you see why?

Hint 4: There are two other right triangles to consider.

Thanks a lot. But really, im not understand this sentence: First construct a perpendicular to AB that runs through C. Call the intersection of this perpendicular and line AB point E. Im not understand where i may construct this line.
And maybe you have some other idea how i can make a plot and solve this.

 

[Deleted member 4993]

Assuming angleBOC = 90 degrees. <<<< You mean angle AOC - right?
HINTS:
a = AB, b = CD, r = radius, u = angleCBO
u = ASIN[1 / SQRT(5)]
r = 4SIN(u)
b = r + SQRT(4 - r^2) ; and you'll find that a = 2b

Since AD = 2r, then area trapezoid
= (3/4)2ra
= 14.4

.

 

[tiigrike]

Denis

My first go round I assumed angle BOC was right, but I could not prove it. Without that proof, I think you can only get to expressing the area of the trapezoid as a function of r.

Really my math teacher said me the angle BOC is not 90 degree.