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Answers
∠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
Step-by-step explanation:
∠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