MathDB

Triangle ratios

Source: UMD 2023 Part II Problem 4

November 30, 2023

geometrytrigonometryratiosimilar triangles

Problem Statement

Assume every side length of a triangle

ABC

is more than

2

and two of its angles are given by

\angle ABC = 57^\circ

and

ACB = 63^\circ

. Point

P

is chosen on side

BC

with

BP:PC = 2:1

. Points

M,N

are chosen on sides

AB

and

AC

, respectively so that

BM = 2

and

CN = 1

. Let

Q

be the point on segment

MN

for which

MQ:QN = 2:1

. Find the value of

PQ

. Your answer must be in simplest form.

Back to Problems View on AoPS