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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