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Byju's Answer
Standard X
Mathematics
Theorem of Geometric Mean
Δ ABC is righ...
Question
Δ
A
B
C
is right angled triangle . if p is the length of the perpendicular from C to AB and a.b.c are the lengths of sides opposite
∠
A
,
∠
B
,
∠
C
,
respectively then prove that
1
p
2
=
1
a
2
+
1
b
2
.
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Solution
R.E.F image
Solution : -
Area of
△
A
B
C
=
1
2
b
a
____(1)
also P is the perpendicular distance
∴
Area
=
1
2
P
C
_____(2)
From (1) & (2)
a
b
=
p
c
___(3)
but we know
C
=
√
a
2
+
b
2
⇒
C
2
=
a
2
+
b
2
Now by (3)
a
2
b
2
=
P
2
C
2
=
P
2
(
a
2
+
b
2
)
⇒
1
P
2
=
a
2
+
b
2
a
2
b
2
=
1
b
2
+
1
a
2
⇒
1
P
2
=
1
a
2
+
1
b
2
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Similar questions
Q.
ABC is a right triangle, right angled at C. If p is the length of perpendicular from C to AB & a, b, c have usual meaning, then prove that
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