MathDB

Let triangle

ABC

acutangle, with

m \angle ACB\leq\ m \angle ABC

M

the midpoint of side

BC

and

P

a point over the side

MC

. Let

C_{1}

the circunference with center

C

. Let

C_{2}

the circunference with center

B

P

is a point of

C_{1}

and

C_{2}

. Let

X

a point on the opposite semiplane than

B

respecting with the straight line

AP

; Let

Y

the intersection of side

XB

with

C_{2}

and

Z

the intersection of side

XC

with

C_{1}

. Let m\angle PAX \equal{} \alpha and m\angle ABC \equal{} \beta. Find the geometric place of

X

if it satisfies the following conditions: (a) \frac {XY}{XZ} \equal{} \frac {XC \plus{} CP}{XB \plus{} BP} (b) \cos(\alpha) \equal{} AB\cdot \frac {\sin(\beta )}{AP}

Problem Statement