Question 199732
Very  interesting  question
Let's  start  with  a  rough  sketch  of  a  circle,  now  one  chord,  now  another  perpendicular  chord  that  goes  thru  center.
This  is  the  situation  that  answers  your  question,  yes  it  can  happen  but  it  does  not have  to.
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The  principle  that  puts  the  second  chord  thru  the  center  is,,,, it  must  be  a  perpendicular  bisector. ALL  perp  bisectors  go  thru center,  hence  could  be  diameters.
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It  is  easy  to  take  your  sketch,  and  just  slide  the  second  chord to  one  side  or  the  other. It   does  not  go  thru  center,  and  is  not  a  diameter.  Your  problem  did  not  specify  bisection.
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Another  interesting  construction,  again  draw  a  rough  circle  and  one  chord.  Draw  a  second  chord, perpendicular  to  first  but  located  at  an  end  of  the  first  chord.  NOW,  if  we  connect  the  other  ends of  the  chord,  we  have  a  triangle.   But,  a  very  special  triangle, it  is  a  right inscribed  triangle,  that  divides  the  circle  into  two  semicircles,  and  has  the  hypotenuse  as  the  diameter.

Good  luck  with  class