MathDB

BT = 2PT wanted, 40-70-70 triangle (2010 Romania District VII P3)

Source:

May 19, 2020

anglesgeometryisoscelesequal segments

Problem Statement

Consider triangle

ABC

with

AB = AC

and

\angle A = 40 ^o

. The points

S

and

T

are on the sides

AB

and

BC

, respectively, so that

\angle BAT = \angle BCS= 10 ^o

. The lines

AT

and

CS

intersect at point

P

. Prove that

BT = 2PT