In an isosceles trapezium ABCD, AB || CD, AB = 9 cm, CD = 12 cm. Points P and Q lie on sides AD and BC respectively such that AP : PD = BQ : QC = 1 : 2. Find the length of PQ.

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.