MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 2
7
7
Part of
2020 LIMIT Category 2
Problems
(1)
Length-Bash geometry
Source: LIMIT 2020 Cat 2 Obj P7
5/25/2020
A circle
D
\mathfrak{D}
D
is drawn through the vertices
A
A
A
and
B
B
B
of
△
A
B
C
\triangle ABC
△
A
BC
. If
D
\mathfrak{D}
D
intersects
A
C
AC
A
C
at a point
M
M
M
and
B
C
BC
BC
at
P
P
P
and
M
P
MP
MP
contains the incenter of
△
A
B
C
\triangle ABC
△
A
BC
, then the length
M
P
MP
MP
is (in standard notation, where
t
=
1
a
+
b
+
c
t=\frac{1}{a+b+c}
t
=
a
+
b
+
c
1
):(A)
a
t
(
b
+
c
)
at(b+c)
a
t
(
b
+
c
)
(B)
c
t
(
b
+
a
)
ct(b+a)
c
t
(
b
+
a
)
(C)
b
c
t
bct
b
c
t
(D)
a
b
t
abt
ab
t
limit
geometry