Question

in the figure O is the centre of the circle prove angle APB-angle BAO=90

Answer 1

In the question given above

According to the figure
In triangle AOB

Angle AOB +  Angle APB = 180
Angle AOB +  (180 - Angle OBA - Angle BAO) = 180
Angle AOB + 180 - Angle OBA - Angle BAO = 180
Angle AOB - Angle OBA - Angle BAO = 0
And Since
angle OBA = 90
Thus
Angle AOB - Angle BAO = 90 deg

Hence Proved