The length of the longest rod that can be placed flat on the floor of a rectangular room is 10 m, and the length of the longest rod that can be placed inside the room from one corner to another is 10√2 m. What is the height of the room?

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.