MathDB

Funny side bash

Source: 2022 Thailand MO Day 2 P9

June 16, 2022

geometry

Problem Statement

Let

PQRS

be a quadrilateral that has an incircle and

PQ\neq QR

. Its incircle touches sides

PQ,QR,RS,

and

T

at

A,B,C,

and

D

, respectively. Line

RP

intersects lines

BA

and

BC

at

T

and

M

, respectively. Place point

N

on line

TB

such that

NM

bisects

\angle TMB

. Lines

CN

and

TM

intersect at

K

, and lines

BK

and

CD

intersect at

H

. Prove that

\angle NMH=90^{\circ}

.

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