USAMO
Guide
Home
Contests
Problemset
Standings
Announcements
…
Back to Problems
Prev
Next
1600
Incircle Radii in Altitude Triangles
Editorial
geometry
right triangles
incircles
In right triangle
A
B
C
ABC
A
B
C
with the right angle at
C
C
C
,
A
C
=
5
AC = 5
A
C
=
5
and
B
C
=
12
BC = 12
B
C
=
12
. Let
H
H
H
be the foot of the altitude from
C
C
C
to
A
B
AB
A
B
. The incircle of triangle
A
C
H
ACH
A
C
H
has radius
r
1
r_1
r
1
and the incircle of triangle
B
C
H
BCH
B
C
H
has radius
r
2
r_2
r
2
. Find
r
1
+
r
2
r_1 + r_2
r
1
+
r
2
.
Sign in to submit your answer
Sign In
