AB and CD are two chords in a circle with centre O, and AD is the diameter. When produced, AB and CD meet at an external point P. If ∠DAP = 27° and ∠APD = 35°, then what is the measure (in degrees) of ∠DBC?

If B is the center of a circle and lines AD and CD are tangent segments drawn from an external point D, then which of the following classifications apply to quadrilateral ABCD? (a) Kite (b) Cyclic quadrilateral (c) Rhombus (d) Trapezium

In a parallelogram PQRS, rays PA and SA are the angle bisectors of ∠QPS and ∠RSP respectively. Find the measure of ∠PAS.