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line BD is tangent to the circumcircle of ADZ

Source: Germany 2001 grade 12 p6

February 23, 2020

geometrytangentcircumcircleright triangle

Problem Statement

Let

ABC

be a triangle with

\angle A = 90^o

and

\angle B < \angle C

. The tangent at

A

to the circumcircle

k

of

\vartriangle ABC

intersects line

BC

at

D

. Let

BY

be the reflection of

A

in

BC

. Also, let

X

be the feet of the perpendicular from

A

to

BE

and let

Y

be the midpoint of

AX

. Line

BY

meets

k

again at

Z

. Prove that line

BD

is tangent to the circumcircle of

\vartriangle ADZ

.

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