Question

In the given figure,PA and PB are two tangents to the circle with the centre O. If angle APB =50°,find:
1.angle AOB
2.angle OAB
3.angle ACB

Answer 1

We know that the radius and tangent are perpendicular at their point of contact

???OBP = ???OAF = 90??

Now, in quadrilateral AOBP:

???A0B + ???OBP + ???APB + ???OAP = 360??

???A0B + 90?? + 50??+ 90?? = 360??

=> 230??+ ???BOC = 360?? ???A0B = 130??

Now, in isosceles triangle AOB,

???A0B + ???OAB + ???OBA = 180??

=> 130?? + 2???OAB = 180??

Therefore, ???OAB = 25??