MathDB

Let

ABCD

be a cyclic quadrilateral, for which

B

and

C

are acute angles.

M

and

N

are the projections of the vertex

B

on the lines

AC

and

AD

, respectively,

P

and

T

are the projections of the vertex

D

on the lines

AB

and

AC

respectively,

Q

and

S

are the intersections of the pairs of lines

MN

and

CD

, and

PT

and

BC

, respectively. Prove the following statements:
a)

NS \parallel PQ \parallel AC

; b)

NP=SQ

; c)

NPQS

is a rectangle if, and only if,

AC

is a diamteter of the circumscribed circle of quadrilateral

ABCD

G4