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Find all possible values of BT/BM

Source: 2015 ISL G4

July 7, 2016

geometry

Problem Statement

Let

ABC

be an acute triangle and let

M

be the midpoint of

AC

. A circle

\omega

passing through

B

and

T

meets the sides

ABC

and

BC

at points

P

and

Q

respectively. Let

T

be the point such that

BPTQ

is a parallelogram. Suppose that

T

lies on the circumcircle of

ABC

. Determine all possible values of

\frac{BT}{BM}

.

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