BOA is adiameter of the circle with centre O and the tangent at a point P meet BA extended at T.If angle ABP=40,Find angle PTA?

given: BOA is a diameter of the circle.PT is the tangent at P.
angle ABP = 40 deg
join PB and PO.
angle BPO = angle OBP=40 deg [angles opposite to equal sides are equal ]
angle OPT = 90 deg [line joining the center to the point of contact is perpendicular to tangent]
angle BPT = 90+40 = 130
in the triangle PBT;
angle PTB = 180 - (angle PBT+angle BPT)
= 180 - (40+130)
= 180 - 170
= 10 deg
hope this helps you.