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Problems
Contests
National and Regional Contests
India Contests
India LIMIT
2020 LIMIT
2020 LIMIT Category 1
18
18
Part of
2020 LIMIT Category 1
Problems
(1)
Squares inscribed in right triangle
Source: LIMIT 2020 Cat 1 Obj P18
5/2/2020
Let
△
A
B
C
\triangle ABC
△
A
BC
be a right triangle with
∠
C
=
9
0
∘
\angle C=90^{\circ}
∠
C
=
9
0
∘
. Two squares
S
1
S_1
S
1
and
S
2
S_2
S
2
are inscribed in the triangle
A
B
C
ABC
A
BC
such that
S
1
S_1
S
1
and
A
B
C
ABC
A
BC
share a common vertex
C
C
C
and
S
2
S_2
S
2
has one of its sides on
A
B
AB
A
B
. Suppose that
Area
(
S
1
)
=
1
+
Area
(
S
2
)
=
441
\text{Area}(S_1)=1+\text{Area}(S_2)=441
Area
(
S
1
)
=
1
+
Area
(
S
2
)
=
441
, then calculate
A
C
+
B
C
AC+BC
A
C
+
BC
(A)
400
400
400
(B)
420
420
420
(C)
441
441
441
(D)
462
462
462
geometry
limit