Answer: BC = 3
Step-by-step explanation:
Given information
OP = 5
AB = 8
BC = x
Determine the length of OB
We know that OB is the radius of the circle and OP is also the radius of the circle
∴ OB = OP = 5
Calculate the length of OC
We know that O is the center of the circle, so it is also the midpoint of AB.
∴ OC = 0.5 AB = (0.5) (8) = 4
Calculate the length of BC
We know that OC and BC are the legs of a right triangle, and OB is the hypotenuse
[tex]BC = \sqrt{OB^{2} -OC^{2} }[/tex]
[tex]BC=\sqrt{(5)^{2} -(4)^{2} }[/tex]
[tex]BC=\sqrt{25 -16 }[/tex]
[tex]BC=\sqrt{9 }=\large\boxed{3}[/tex]
Hope this helps!! :)
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