Question

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Answer 1

Join OP and OQ

∠OPR = ∠OQR = 90° ---- 1 



And in ΔOPR and ΔOQR 



∠OPR = ∠ OQR = 90° (from equation 1) 



OP = OQ (Radii of same circle) 



And  



OR = OR (common side) 



ΔOPR = ΔOQR (ByRHS Congruency) 



So, RP = RQ --- 2 



And  ∠ORP = ∠ORQ --- 3 



∠PRQ = ∠ORP + ∠ORQ 



Substitute ∠PQR = 120° (given)  



And from equation 3 we get 



∠ORP + ∠ORP = 120° 



2 ∠ORP = 120° 



∠ORP = 60° 



And we know cos 0 = Adjacent/hypotenuse 



So in ΔOPR we get  



Cos ∠ORP = PR/OR 



Cos 60° = PR/OR 



½ = PR/OR (we know cos 60° = ½) 



OR = 2PR 



OR = PR + PR (substitute value from equation 2 we get) 



OR = PR  + RQ

Answer 2

hope it will work.....