1. BAC= 90, <s in a semi circle
E2= 90, line drawn from centre to midpoint of chord
Therefore BA I I OD
O1=x, corresp <s equal, AB parallel to OD
A1 = O1
therefore AOCD is a cyclic quad , converse theorem of <s in the same segment.
3. AOC =2x ,< at centre = 2 x < at circumf.
O1=x and also O2 = X
C2=O2=x, <s in same segment
therefore DC is a tangent to circle, converse of ta-chord theorem