MathDB

SMT 2021 Geometry Tiebreaker #3

Source:

August 9, 2023

geometry

Problem Statement

In quadrilateral

ABCD

,

CD = 14

,

\angle BAD = 105^o

,

\angle ACD = 35^o

, and

\angle ACB = 40^o

. Let the midpoint of

CD

be

M

. Points

P

and

Q

lie on

\overrightarrow{AM}

and

\overrightarrow{BM}

, respectively, such that

CD

and

\angle AQB = 40^o

.

P B

intersects

CD

at point

R

and

QA

intersects

CD

at point

S

. If

CR = 2

, what is the length of

SM

?

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