MathDB
Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 1
11
Circle tangent to side at vertex
Circle tangent to side at vertex
Source: LIMIT 2020 Cat 1 Obj P11
May 2, 2020
geometry
limit
Problem Statement
In
△
A
B
C
\triangle ABC
△
A
BC
,
∠
A
=
3
0
∘
\angle A=30^{\circ}
∠
A
=
3
0
∘
,
B
C
=
13
BC=13
BC
=
13
. Given
2
2
2
circles
γ
1
,
γ
2
\gamma_1, \gamma_2
γ
1
,
γ
2
ith radius
r
1
,
r
2
r_1,r_2
r
1
,
r
2
contain
A
A
A
and touch
B
C
BC
BC
at
B
B
B
and
C
C
C
respectively. Find
r
1
r
2
r_1r_2
r
1
r
2
.
Back to Problems
View on AoPS