O is the centre of the circle and TP is the tange

Question

O is the centre of the circle and TP is the tangent to the circle from an external point T. If angle PBT = 30 degree , prove that BA : AT = 2 : 1

Anwesha Barman · Accepted Answer

Hi, I’m not able to upload the diagram ….anyway, here’s the solution.Construction : Join P and O to get POProof : Let Radius = r => BO=PO=AO=r POA =2 PBA=2 x 30o = 60o [ at centre is twice the subtended on the circle.]BPA = 90o [ in semicircle.]PAB = 30o [ by sum prop. in PAB ]InPOA,180 - (O + A) =P => P =60o Therefore, POA is euilateral.Hence, PA=PO=AP =r In OPT, O =60o , P = 90o [tangent perpendicular to radius]By sum prop., T = 30oOn comparing, BPA TPO { above angles and PO=PA=r} byASA testBy CPCT, BA=TOBO+OA=OA+TA2r=r + TATA=rBA/AT = 2r/r =2/1 = 2:1. …............proved.Hope it helps....... :)

10 grade maths> O is the centre of the circle and TP is t...

O is the centre of the circle and TP is the tangent to the circle from an external point T. If angle PBT = 30 degree , prove that BA : AT = 2 : 1

Abrar Syed , 9 Years ago

Anwesha Barman

Yash Chourasiya

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10 grade maths> O is the centre of the circle and TP is t...

O is the centre of the circle and TP is the tangent to the circle from an external point T. If angle PBT = 30 degree , prove that BA : AT = 2 : 1

Abrar Syed , 9 Years ago

Anwesha Barman

Yash Chourasiya

LIVE ONLINE CLASSES

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