CB is the diameter of this circle and its radius is 1.13 cm.AC = 1.82 cmThe length of AB correct to one decimal place is:

Given that CB is the diameter and AC = 1.82 cm, we can use the Pythagorean theorem to find the length of AB. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

In this case, the hypotenuse is CB (the diameter), and we know that the radius is half of the diameter, so the length of CB is 2 * 1.13 cm = 2.26 cm.

One of the other sides is AC, which is given as 1.82 cm. We'll call this 'a'. We're trying to find the length of AB, which we'll call 'b'.

So we can set up the equation as follows:

(1.82 cm)² + b² = (2.26 cm)²

Solving for 'b' gives:

b² = (2.26 cm)² - (1.82 cm)² b² = 5.1076 cm² - 3.3124 cm² b² = 1.7952 cm²

Taking the square root of both sides gives:

b = √1.7952 cm b = 1.34 cm

So the length of AB, correct to one decimal place, is 1.3 cm.