In triangle ABC, the bisector of angle BAC meets BC at point D in such a way that AB = 10 cm, AC = 15 cm, and BD = 6 cm. Find the length of BC (in cm).

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.