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Undescribed triangle?

Source: Sharygin 2019 Finals Day 1 Grade 9 P1

July 30, 2019

geometrySharygin Geometry Olympiad

Problem Statement

A triangle

OAB

with

\angle A=90^{\circ}

lies inside another triangle with vertex

O

. The altitude of

OAB

from

A

until it meets the side of angle

O

at

M

. The distances from

M

and

B

to the second side of angle

O

are

2

and

1

respectively. Find the length of

OA

.

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