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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2005 Sharygin Geometry Olympiad
11.4
11.4
Part of
2005 Sharygin Geometry Olympiad
Problems
(1)
find chord of one circle tangent to another one, incircle related
Source: Sharygin 2005 finals 11.4
8/31/2019
In the triangle
A
B
C
,
∠
A
=
α
,
B
C
=
a
ABC , \angle A = \alpha, BC = a
A
BC
,
∠
A
=
α
,
BC
=
a
. The inscribed circle touches the lines
A
B
AB
A
B
and
A
C
AC
A
C
at points
M
M
M
and
P
P
P
. Find the length of the chord cut by the line
M
P
MP
MP
in a circle with diameter
B
C
BC
BC
.
geometry
angle
incircle
chord
diameter