Given that line AC is perpendicular to the circle centered at O with a radius of 1 unit, and the length of AC is 1.5 units, we can find the length of segment AB using the Pythagorean theorem.
Let's denote the length of segment AB as x.
Since AC is a diameter of the circle, its length is twice the radius, which is 2 units. However, in this case, the length of AC is given as 1.5 units.
Now, we have a right triangle formed by segments AO, OB, and AB. AO and OB are both radii of the circle, each measuring 1 unit.
Applying the Pythagorean theorem, we can write the equation: AO^2 + OB^2 = AB^2.
Substituting the known values, we get: 1^2 + 1^2 = AB^2.
Simplifying, we have: 1 + 1 = AB^2.
This gives us: AB^2 = 2.
Taking the square root of both sides, we find: AB = √2 units.
Therefore, the length of segment AB is approximately 1.41 units.o
