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angles equal 180

Source: Olimpiada Rioplatense 2015-Level 3-Problem 1

July 1, 2016

geometry

Problem Statement

Let

ABC

be a triangle and

P

a point on the side

BC

. Let

S_1

be the circumference with center

B

and radius

BP

that cuts the side

AB

at

D

such that

D

lies between

A

and

B

. Let

S_2

be the circumference with center

C

and radius

CP

that cuts the side

AC

at

E

such that

E

lies between

A

and

C

. Line

AP

cuts

S_1

and

S_2

at

X

and

Y

different from

P

, respectively. We call

T

the point of intersection of

DX

and

EY

. Prove that

\angle BAC+ 2 \angle DTE=180

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