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Byju's Answer
Standard VII
Mathematics
Equal Angles Subtend Equal Sides
BL and CM a...
Question
B
L
and
C
M
are medians of
Δ
A
B
C
right angled at
A
. Prove that
4
(
B
L
2
+
C
M
2
)
=
5
B
C
2
.
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Solution
G
i
v
e
n
:
△
A
B
C
i
s
r
i
g
h
t
a
n
g
l
e
d
a
t
A
.
B
L
a
n
d
C
M
a
r
e
i
t
s
m
e
d
i
a
n
s
T
o
P
r
o
v
e
:
P
r
o
o
f
:
I
n
△
B
A
L
B
L
2
=
A
L
2
+
A
B
2
.
.
.
(
1
)
[
U
s
i
n
g
P
y
t
h
a
g
o
r
a
s
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o
r
e
m
]
I
n
△
C
A
M
C
M
2
=
A
M
2
+
A
C
2
.
.
.
.
.
(
2
)
[
U
s
i
n
g
P
y
t
h
a
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h
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]
A
d
d
i
n
g
(
1
)
a
n
d
(
2
)
a
n
d
t
h
e
n
m
u
l
t
i
p
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y
i
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g
b
y
4
,
w
e
g
e
t
4
(
B
L
2
+
C
M
2
)
=
4
(
A
L
2
+
A
B
2
+
A
M
2
+
A
C
2
)
=
4
A
L
2
+
A
M
2
+
(
A
B
2
+
A
C
2
)
=
4
A
L
2
+
A
M
2
+
B
C
2
[
I
n
r
i
g
h
t
a
n
g
l
e
A
B
C
A
B
2
+
A
C
2
=
B
C
2
]
=
4
(
A
L
2
+
A
M
2
+
B
C
2
)
=
4
(
M
L
2
+
B
C
2
)
[
I
n
L
A
M
A
L
2
+
A
M
2
=
M
L
2
]
=
4
M
L
2
+
4
B
C
2
[
A
c
c
o
r
d
i
n
g
t
o
m
i
d
p
o
i
n
t
t
h
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r
m
a
l
i
n
e
j
o
i
n
i
n
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m
i
d
−
p
o
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t
s
o
f
t
w
o
s
i
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s
p
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a
n
d
i
s
e
q
u
a
l
t
o
h
a
l
f
o
f
i
t
,
M
L
=
B
C
2
]
=
B
C
2
+
4
B
C
2
=
5
B
C
2
.
H
e
n
c
e
p
r
o
v
e
d
.\quad
Suggest Corrections
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Similar questions
Q.
In the fifure
B
L
&
C
M
are the medians of
Δ
A
B
C
, right angled at
A
. Prove that
4
(
B
L
2
+
C
M
2
)
=
5
B
C
2
.
Q.
BL and CM are medians of triangle ABC right angled at A , prove
4
(
B
L
2
+
C
M
2
)
=
5
B
C
2
Q.
BL and CM are medians of a triangle ABC right angled at A. Prove that
4
(
B
L
2
+
C
M
2
)
=
5
B
C
2
. [3 MARKS]
Q.
In ∆ABC, ∠BAC = 90°, seg BL and seg CM are medians of ∆ABC. Then prove that:
4(BL
2
+ CM
2
) = 5 BC
2