Explanation

In this figure, if \(<BDC = 90\) degrees than \(<BDO\) should be \(90\) degrees as well.
This is because angle in a straight line add to \(180\) degree

Similarly, If \(<AOB = 44\)degrees than \(<BOD = 46\) degrees because Given \(AOC\) is a right triangle so \(<AOB\) and \(<BOD\) should add to \(90\)degrees

Now the remaining angle\(<DBO = 44\) degrees
Sum of angles in a triangle add to \(180\) degrees.

From here we can deduce that \(BD>OD\) because side opposite larger angle is larger than side opposite smaller angle in a triangle
option B
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes