Final answer:
The length of the radius is 2 units and the length of the diameter is 4 units.
Step-by-step explanation:
To find the length of the radius and diameter of the circle, we can use the fact that the diameter is twice the length of the radius. So, if TO is the diameter of the circle, 3x+5 = 2r, where r is the radius. Similarly, if TL is the diameter, 5x+11 = 2r.
To solve for r, we can solve the equations for x and substitute the value into the equation for r. First, solve the equation 5x+11 = 2r for x:
5x = 2r - 11
x = (2r - 11)/5
Next, substitute the value of x into the equation 3x+5 = 2r:
3((2r - 11)/5) + 5 = 2r
Simplify the equation:
(6r - 33)/5 + 5 = 2r
Multiply both sides of the equation by 5:
6r - 33 + 25 = 10r
Combine like terms:
6r + 8 = 10r
Subtract 6r from both sides of the equation:
8 = 4r
Divide both sides of the equation by 4:
r = 2
The length of the radius of the circle is 2 units. To find the length of the diameter, simply double the length of the radius:
Diameter = 2 * 2 = 4 units.