Question

AOB is a diameter of the circle and P is any point on the circle find angle APB

Answer 1

in the given circle,
AOB is the diameter
P is any point on the circle
therefore arc APB forms a semicircle and angle APB is inscribed in it
we know that, any angle inscribed in a semicircle measures 90degree
therefore angle APB measures 90degree
OR
By inscribed angle theorem,
angle APB = 1/2 × it's corresponding arc i.e. arc AOB
Since Arc AOB forms semicircle, Arc AOB= 180 degree
therefore angle APB = 1/2 × 180
Therefore angle APB = 90degree (by inscribed angle theorem)