In a triangle ABC, AB = 6 cm and AC = 9 cm. If AD is the internal bisector of angle BAC and it meets BC at D such that BC = 10 cm, find the length (in cm) of BD.

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.