In the given diagram we can see that the length of the circle's radius is 8. In the exercise we are also given that the chord has a length of 13.5.
Since the chord and the diameter are perpendicular, we know that the diameter bisects the chord. This fact will help us find lengths later in the exercise. Now, let's draw a radius in order to have a right triangle. Keep in mind that since the radius is constant, its length is always 8.
Finally, we will pay close attention to the right triangle we have just drawn. Be aware of the fact that the chord being bisected tells us that the length of the horizontal leg is half that of the chord.
Chord length/Bisected → 13.5/2= 6.75
In the right triangle the hypotenuse has a length of 8 and the horizontal leg has a length of 6.75. We want to find the length of the vertical leg.
To find the length of BD we will substitute these values into the Pythagorean Theorem.
