In the image point a is the center of the which two line segment must be equal in length

Answer choices to this question are :

1. AH¯¯¯¯¯ and BC¯¯¯¯¯ 

2. HI¯¯¯¯ and BC¯¯¯¯¯ 

3. EF¯¯¯¯¯ and HI¯¯¯¯ 

4. EF¯¯¯¯¯ and AI¯¯¯¯

The correct answer choice is: 

3. EF¯¯¯¯¯ and HI¯¯¯¯ 

The lines EF and HI, both, are passing through the point A which is the center of the circle. Both lines are, therefore, diameters of the circle, that means 
EF = HI