Question

What is the length of chord AB

Answer 1

Imagine an xy system on top of the origin of the circle. Then the y coordinate of B is 3-2.25 = 0.75.

Suppose there is a line from the center to B. Line OA has an angle alpha with the x axis. Simple trigonometry tells us that 3*sin(alpha) = 0.75.

And it also tells us that line AB would be 2*3*cos(alpha).

So AB = 6*cos( arcsin(0.75/3) ) ≈ 5.8

Thank god that is in the list as answer C!!

Answer 2

The answer is the option C

`5.8\ ft`

Explanation:

see the attached figure with letters to better understand the problem

we know that

In the right triangle ACD

Applying the Pythagoras Theorem

`AC^(2) =CD^(2)+AD^(2)`

Solve for AD

`AD^(2)=AC^(2)-CD^(2)`

in this problem we have

`AC=r=3\ ft`

`CD=3-2.25=0.75\ ft`

substitute

`AD^(2)=3^(2)-0.75^(2)`

`AD=2.90\ ft`

`AB=2AD`

`AB=2(2.90)=5.80\ ft`