Proofs of the Theorems on Circumscribable Quadrilaterals

Please help me to have some proofs of the theorems related to CIRCUMSCRIBABLE QUADRILATERALS.

Here are some of the THEOREMS that needs to be proven;

**THEOREM (5): ***A point is on the angle bisector of the angle if and only if the points is equidistant from the sides of the angle, that is, if and only if the lengths of the perpendicular segments from the point to the sides of the angle are equal.*

**THEOREM (6): ***The four angle bisectors of a quadrilateral are concurrent if and only if the quadrilateral is circumscribable.*

**THEOREM (7): ***A quadrilateral is circumscribable if and only if the incircles of the two triangles formed by a diagonal are tangent to each other.*

**THEOREM (8): ***The four sides of a circumscribable quadrilateral intersect the incircles of the two triangles formed by a diagonal of the quadrilateral to form four points, all of which are on a circle taht is concentric with the quadrilateral's inscribed circle.*

**THANK YOU VERY MUCH AND I HOPE TO SEE THE PROOFS AS SOON AS POSSIBLE. THANK YOU!**