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Cyclic Quadrilaterals

Theorem8

angle P + angle R= 180 degree and angle Q + angle S= 180 degree. [Reference: opp. angles, cyclic quad.]

Theorem9

y=x. [Reference: ext. angle, cyclic quad.]

Theorem10( Converse of Theorem7)

If x=y, then A, B, Q, P are concyclic. [Reference: converse of angles in the same segment]

Theorem11( Converse of Theorem8)

If angle P + angle R= 180 degree or angle Q + angle S= 180 degree,

then P, Q, R, S are concyclic. [Reference: opp. angles supp.]

Theorem12( Converse of Theorem9)

If y=x, then P, Q, R, S are concyclic. [Reference: ext. angle= int. opp. angle]