Solution- Given=TP is the tangent to the circle with centreO. T is an external point on the circle AND angle PBT=30. To prove-BA:AT=2:1. Proof-???????Angle AOP=30*=60 Angle OAP=180-30-90=60 therefore,OP=PA also Angle ATP=Angle APT=30 therefore,AP=AT=OP=OA Hence,BA=2,OA=2 at BA:AT=2:1…....................…………………....Hence proved.

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