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Two tangents PA and PB are drawn to the circle with center O, such that ∠APB=120o. Prove that OP=2AP.
Ans: Given : - ∠APB = 120o Construction : -Join OP To prove : -OP = 2AP
Proof :- ∠APB = 120o
∴∠APO = ∠OPB = 60o
Cos 60o = AP/OP
1/2 = AP/OP
∴OP = 2AP
Hence proved
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f(x)+f(x+1/2) =1 f(x)=1-f(x+1/2) 0∫2f(x)dx=0∫21-f(x+1/2)dx 0∫2f(x)dx=2-0∫2f(x+1/2)dx take (x+1/2)=v dx=dv 0∫2f(v)dv=2-0∫2f(v)dv 2(0∫2f(v)dv)=2 0∫2f(v)dv=1 0∫2f(x)dx=1
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