Anwesha Barman
Last Activity: 9 Years ago
Hi, I’m not able to upload the diagram ….anyway, here’s the solution.
Construction : Join P and O to get PO
Proof : Let Radius = r => BO=PO=AO=r

POA =2

PBA=2 x 30
o = 60
o [

at centre is twice the

subtended on the circle.]

BPA = 90
o [

in semicircle.]


PAB = 30
o [ by

sum prop. in

PAB ]
Therefore,

POA is euilateral.
Hence, PA=PO=AP =r
In

OPT,

O =60
o ,

P = 90
o [tangent perpendicular to radius]
By

sum prop.,

T = 30
oOn comparing,

BPA


TPO { above angles and PO=PA=r} byASA test
By CPCT, BA=TO
BO+OA=OA+TA
2r=r + TA
TA=r
BA/AT = 2r/r =2/1 = 2:1. …............proved.
Hope it helps....... :)