Two tangents are drawn from a point P on the circle with centre at O, touching the circle at point Q and T respectively. Another tangent AB touches the circle at point S. If angle QPT =55°, find the angle AOB= ?

Since PQ and PT are tangent on circle so $$\angle$$PQO = $$\angle$$PTO = 90

In quadrilateral PQOT   $$\angle$$PQO+$$\angle$$PTO+$$\angle$$QOT+$$\angle$$TPQ = 360

                                                           90+90+$$\angle$$QOT+55 =360

                                                           $$\angle$$QOT = 125

Since AB touches the circle hence OA and OB are the angle bisector of $$\angle$$QOS and $$\angle$$TOS respectively.

                                 So $$\angle$$AOB = $$\frac{1}{2}\angle$$QOT = $$\frac{125}{2}$$ = 62.5