Manas has drawn a circle with centre O of which AB is a chord. A tangent is drawn at the point B which intersects extended AO at the point. T. If `angle BAT=21^(@),` find the value of `angle BTA.`

Explanation

Given that `angle BAT=21^(@)`
`therefore angle OBA =21^(@) [because OA=OB,` radii of same circle]
Again, BT is a tangent at B of the cirxcle with centre O and OB is a radius passing through B.
`therefore OB bot BT, therefore angle OBT=90^(@)`
Now `angle ABT=angle ABO+angle OBT`
`=21^(@) +90^(@) [angle OBA =21^(@)and angle OBT=90^(@)]=111^(@)`
Then `angle BAT=180^(@) -(angle BAT+angle ABT+angle ABT)[because` sum of three angles of a triangle is `180^(@)`]
`=180^(@)-(21^(@)+111^(@))=180^(@) -132^(@) =48^(@)`
Hence `angle BAT=48^(@).`