Please help me in solving this question

Dear Student

Given

AB   =  CD   , And M and N are the mid point of AB and CD respectively . 



We know " ​Equal chords are equidistant from the centre . "
So,
OM  = ON 
So,
$\angle$ OMN  = $\angle$ ONM                                                         --------- ( 1 )               ( Angles opposite to equal sides )
And
We know " ​The line segment drawn from the centre to the midpoint of the chord is perpendicular to the chord. "
So,
$\angle$ OMA = $\angle$ OMB  = $\angle$ ONC = $\angle$ OND  = 90$°$                ---------- ( 2 )

1 ) $\angle$ ​BMN  = $\angle$ OMB  - $\angle$ OMN                                    ---------- ( 3 )

And
$\angle$ DNM  = $\angle$ OND - $\angle$ ONM 
By equation 1 and equation 2 , we get 
$\angle$ DNM = $\angle$ OMB  - $\angle$ OMN                                        ------------- ( 4 )

We can see that equation 3 and equation 4 are equal ,So

$\angle$ BMN  = $\angle$ DNM                                                       ( Hence proved )

2 ) $\angle$ AMN  = $\angle$ OMA  + $\angle$ OMN                                --------------- ( 5 )
And
$\angle$ CNM  = $\angle$ ONC  + $\angle$ ONM
By equation 1 and equation 2 , we get 
$\angle$ CNM = $\angle$ OMA + $\angle$ OMN                                       ------------- ( 6 )

We can see that equation 5 and equation 6 are equal ,So

$\angle$ AMN = $\angle$ CNM                                                      ( Hence proved )

Regards​​​​