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

Answer:

The answer is the option C

$5.8\ ft$

Step-by-step 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

$AD^{2}=3^{2}-0.75^{2}$

$AD=2.90\ ft$

$AB=2AD$

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