ANSWER
The length of a Diameter is 3.714
EXPLANATION
The circumscribed triangle is shown in the attachment.
We use the cosine ratio to find the altitude of the isosceles triangle.


Altitude =8cos(60°)
Altitude=4cm
Let the upper half of the altitude be y cm.
Then the radius of the circle is (y-4)cm
The upper radius meets the tangent at right angles.
From the smaller right triangle,






y=1.857
The diameter is 2y

=2(1.875)
The length of a Diameter is 3.714
Answer:
x = 6/5 or x = -2
Step-by-step explanation:
We need to solve:
|5x+2|=8
We know that |u|=a the u = a and u = -a
Now solving:
|5x+2|=8
5x +2 = 8 or 5x +2 = -8
5x = 8-2 or 5x = -8-2
5x = 6 or 5x = -10
x = 6/5 or x = -10/5
x = 6/5 or x = -2
So, x = 6/5 or x = -2
A is the mid point ==> AL = AB = 2AB
6x-17=2(2x+3) => 6x -17 = 4x +6 => 2x = 23 =>x=23/2
then just plug x into LB and AB
22 I think If I worked it out right