Answer :

(i) To understand alternate segment following diagram is beneficial:



Angles with same color are equal.


Theorem:


The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment.


The alternate segment for BAQ is ADB.


(ii) The alternate segment for DAP is ABD


(iii) The figure is as follows:



When C will be jointed to B then ACB will be equal to BAP.


(iv) ABD and ADB are equal to DAP and BAQ because angles in alternate segments are equal.


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