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Byju's Answer
Standard VII
Mathematics
Equal Angles Subtend Equal Sides
In Figure, O ...
Question
In Figure, O is a point in the interior of a triangle ABC, OD
⊥
BC, OE
⊥
AC and OF
⊥
AB. Show that
O
A
2
+
O
B
2
+
O
C
2
−
O
D
2
−
O
E
2
−
O
F
2
=
A
F
2
+
B
D
2
+
C
E
2
.
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Solution
From the all the right angled triangles, we get
O
A
2
=
A
F
2
+
O
F
2
O
B
2
=
O
D
2
+
B
D
2
O
C
2
=
O
E
2
+
E
C
2
We have,
A
F
2
+
B
D
2
+
C
E
2
=
O
A
2
−
O
F
2
+
O
B
2
−
O
D
2
+
O
C
2
−
O
E
2
⟹
(
O
A
2
−
O
E
2
)
+
(
O
B
2
−
O
F
2
)
+
(
O
C
2
−
O
D
2
)
. Hence proved.
Suggest Corrections
0
Similar questions
Q.
In Fig.,
O
is a point in the interior of a triangle
A
B
C
,
O
D
⊥
B
C
,
O
E
⊥
A
C
and
O
F
⊥
A
B
. Show that
(i)
O
A
2
+
O
B
2
+
O
C
2
−
O
D
2
−
O
E
2
−
O
F
2
=
A
F
2
+
B
D
2
+
C
E
2
,
(ii)
A
F
2
+
B
D
2
+
C
E
2
=
A
E
2
+
C
D
2
+
B
F
2
.
Q.
In the given figure, O is a point in the interior of a triangle ABC, OD
⊥
BC, OE
⊥
AC and OF
⊥
AB.
Show that
O
A
2
+
O
B
2
+
O
C
2
−
O
D
2
−
O
E
2
−
O
F
2
=
A
F
2
+
B
D
2
+
C
E
2
Q.
Question 8 (i)
In the given figure, O is a point in the interior of a triangle
ABC, OD \(\perp\) BC, OE \(\perp\) AC and OF \(\perp\) AB.
Show that \((i) OA^2 + OB^2 + OC^2 - OD^2 - OE^2 - OF^2 = AF^2 + BD^2 + CE^2\)
Q.
In the above figure,
O
is a point in the interior of a triangle
A
B
C
,
O
D
⊥
B
C
,
O
E
⊥
A
C
and
O
F
⊥
A
B
. Show that:
(i)
O
A
2
+
O
B
2
+
O
C
2
−
O
D
2
−
O
E
2
−
O
F
2
=
A
F
2
+
B
D
2
+
C
E
2
(ii)
A
F
2
+
B
D
2
+
C
E
2
=
A
E
2
+
C
D
2
+
B
F
2
Q.
In the given figure, O is a point in the interior of a
△
A
B
C
, OD
⊥
BC, OE
⊥
AC and OF
⊥
AB. Then,
O
A
2
+
O
B
2
+
O
C
2
−
O
D
2
−
O
E
2
−
O
F
2
=
A
F
2
−
B
D
2
−
C
E
2
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