

1) ∠POM = ∠OPM + ∠ORP  1) By exterior angle theorem (∠POM is exterior angle) 
2) OP = OR  2) Radii of same circle 
3) ∠OPR = ∠ORP  3) In a Δ two sides are equal then the angle opposite to them are also equal. 
4) ∠POM = ∠ORP + ∠ORP  4) Substitution property. From (1) 
5) ∠POM = 2∠ORP  5) Addition property. 


1) ∠POM = ∠OPR + ∠ORP  1) Exterior angle theorem. 
2) ∠POM = ∠ORP + ∠ORP  2) As,OP = OR = radius. ∴∠ORQ = ∠ORP 
3) ∠POM = 2∠ORP  3) Substitution and addition property. 
4) ∠QOM = ∠ORQ + ∠OQR  4) Exterior angle theorem. 
5) ∠QOM = ∠ORQ + ∠ORQ  5) As, OQ =OR = radius, ∴ ∠ORQ = ∠OQR 
6) ∠QOM = 2∠ORQ  6) Substitution and addition property. 


1) ∠POM = ∠OPR + ∠ ORP  1) By exterior angle theorem. 
2) ∠POM = 2∠ORP  2) As, OP = OR = radius, ∴∠OPR = ∠ORP and by addition property 
3) ∠ QOM = ∠ORQ + ∠OQR  3) By exterior angle theorem in ΔQOR 
4) ∠QOM = 2∠ORQ  4) As, OP = OR = radius, ∴∠ORQ = ∠OQR and by addition property 
5) ∠POM + ∠QOM = 2(∠ORP + ∠ORQ)  5) From (2) and (4) 
6) Reflex ∠POQ = 2∠PRQ  6) Reflex of ∠POQ =∠POM + ∠QOM 


1) ∠POQ = 2∠PRQ  1) Angle subtended by an arc of a circle at its center is twice the angle formed by the same arc. 
2) 180 ^{0} = 2∠PRQ  2) As POQ is a straight line 
3) ∴ ∠PRQ = 90 ^{0}  3) Division property 