Radius of circle is straight line segment connecting the center of circle to its circumference. The length of AB for given context is: |AB| = 24.9 units.
The Pythagoras theorem:
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |PQ| means length of line segment PQ
What is the relation between line perpendicular to chord from the center of circle?
If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
For given case, we're given that:
- Length of radius of circle = 18 units = |OB| (as OB is a radius)
- Length of OC = |OC| = 13 units
- To find: Length of AB = |AB| = |AC| + |CB| = 2|CB| (by aforesaid relation, as C will bisect the line segment AB)
Since we've got OCB as right angled triangle(a triangle with one of the angle as of right angled (90 degrees) ), thus, using Pythagoras theorem, we get:
[tex](|OB|)^2 = (|OC|)^2 + (|CB|)^2 \\18^2 = 13^2 + (|CB|)^2\\\\|CB| = \sqrt{18^2 - 13^2} \text{ \: Positive root as length is non-negative quantity}\\\\|CB| = \sqrt{155} \approx 12.45 \: \rm units[/tex]
Thus, we get:
|AB| = 2|CB| ≈ 24.9 units
Thus, The length of AB for given context is: |AB| = 24.9 units.
Learn more about Pythagoras theorem here:
https://brainly.com/question/12237712
