Extend the segment that goes from the center of the circle to the chord, and draw a diameter. If the chord and the diameter are perpendicular, then the diameter bisects the chord.
≈ 6.7
Practice makes perfect
Consider the given circle. We will find the value of y.
In the diagram, we can extend the segment that goes from the center of the circle to the chord with the given length, and draw a diameter.
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 y.
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 one of the legs is 4.5.
Chord length/Bisected → 9/2= 4.5
The other leg's length is given to be 5. We want to find the length of the hypotenuse y.
To find the value of y, we will substitute these values into the Pythagorean Theorem.
