MathDB

Let

ABC

be a triangle with

AC > AB

. Let

P

be the intersection point of the perpendicular bisector of

BC

and the internal angle bisector of

\angle{A}

. Construct points

X

AB

(extended) and

Y

AC

such that

PX

is perpendicular to

AB

and

PY

is perpendicular to

AC

. Let

Z

be the intersection point of

XY

and

BC

. Determine the value of

\frac{BZ}{ZC}

3