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2007 Harvard-MIT Mathematics Tournament
30
30
Part of
2007 Harvard-MIT Mathematics Tournament
Problems
(1)
2007 Guts #30: Feet of the Perpendiculars of the Cyclic Quad
Source:
6/22/2012
A
B
C
D
ABCD
A
BC
D
is a cyclic quadrilateral in which
A
B
=
3
AB=3
A
B
=
3
,
B
C
=
5
BC=5
BC
=
5
,
C
D
=
6
CD=6
C
D
=
6
, and
A
D
=
10
AD=10
A
D
=
10
.
M
M
M
,
I
I
I
, and
T
T
T
are the feet of the perpendiculars from
D
D
D
to lines
A
B
AB
A
B
,
A
C
AC
A
C
, and
B
C
BC
BC
respectively. Determine the value of
M
I
/
I
T
MI/IT
M
I
/
I
T
.
geometry
circumcircle
cyclic quadrilateral