1) OL ⊥ AB ⇒ AL = 1/2AB  1) OM ⊥ CD ⇒ CM = 1/2CD 
2) AB = CD  2) Given 
3) 1/2 AB = 1/2 CD  3) Given 
4) AL = CM  4) From AB = CD 
5) OA = OC  5) Equal radius of the circle 
6) AL = CM  6) From (4 ) 
7) ∠ALO = ∠CMO  7) Each 90^{0} 
8) OL = OM  8) CPCTC 


1) AB = CD  1) Given 
2) OA = OC  2) Radius of same circle 
3) OB = OD  3) Radius of same circle 
4) ΔAOB = ΔCOD  4) SSS Postulate 
5) ∠AOB = ∠COD  5) CPCTC 


1) ∠POQ = 2∠PRQ  1) Given 
2) ∠POQ = 2∠PSQ  2) Given 
3) 2∠PRQ = 2∠PSQ  3) From (1) and (2) 
4) ∴ ∠PRQ = ∠PSQ  4) From (3) 
5) Reflex ∠POQ = 2∠PRQ and Reflex ∠POQ = 2∠PSQ  5) From the diagram 
6) 2∠PRQ = 2∠PSQ  6) From the diagram 
7) ∠PRQ = ∠PSQ  7) From (6) 