MathDB

angle chasing, <ABK = <CBL = 2a - 180^o, <ABC=a, angle bisector

Source: V Soros Olympiad 1998-99 Round 2 11.6 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

May 25, 2024

geometryanglesangle bisector

Problem Statement

In triangle

ABC

, angle

B

is obtuse and equal to

a

. The bisectors of angles

A

and

C

intersect opposite sides at points

P

and

M

, respectively. On the side

AC

, points

K

and

L

are taken so that

\angle ABK = \angle CBL = 2a - 180^o

. What is the angle between straight lines

KP

and

LM