Answer:
[tex]\qquad\qquad\qquad\boxed{ \sf{ \: \bf \: \: (A) \: \: 8 \: cm \: \: }}\\ \\ [/tex]
Step-by-step explanation:
Before we start the question, let's recall
Radius of a circle :- A line segment drawn from the center to its circumference. In the given figure, OA, OB, OC are radius of circle.
Diameter of a circle :- A line segment intersects the circle in two points and passing through the center of circle. Diameter is basically twice the radius of circle.
Let's solve the problem now!!!
Given that, O is center of a circle.
As A, B, C are points on the circumference of a circle.
[tex]\sf\implies \sf \:OA = OB = OC \\ \\ [/tex]
It is given that,
[tex]\sf \: OC = 4 \: cm \\ \\ [/tex]
So,
[tex]\sf\implies \sf \:OA = OB = 4 \: cm \\ \\ [/tex]
Now, Consider
[tex]\bf \: \: AB \\ \\ [/tex]
[tex]\qquad\sf \: = OA + OB \\ \\ [/tex]
[tex]\qquad\sf \: = OA + OA\\ \\ [/tex]
[tex]\qquad\sf \: = 2OA\\ \\ [/tex]
[tex]\qquad\sf \: = 2 \times 4\\ \\ [/tex]
[tex]\qquad\sf \: = 8 \: cm\\ \\ [/tex]
Hence,
[tex]\sf\implies \bf \: \: AB \: = \: 8 \: cm\\ \\ [/tex]