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National and Regional Contests
Albania Contests
Albania Round 2
2014 Albania Round 2
3
3
Part of
2014 Albania Round 2
Problems
(1)
Radii of incircles in right angled triangle.......easy geometry
Source: Albania Round 2, Grade XI 2014 P3
11/14/2018
In a right
Δ
A
B
C
\Delta ABC
Δ
A
BC
(
∠
C
=
9
0
∘
\angle C = 90^{\circ}
∠
C
=
9
0
∘
),
C
D
CD
C
D
is the height. Let
r
1
r_1
r
1
and
r
2
r_2
r
2
be the radii of inscribed circles of
Δ
A
C
D
\Delta ACD
Δ
A
C
D
and
Δ
D
C
B
\Delta DCB
Δ
D
CB
. Find the radius of inscribed circle of
Δ
A
B
C
\Delta ABC
Δ
A
BC
geometry