in triangle ABC LC = 90° AB = c AC = a BC = CD AB , CD = p then prove that cp =ab
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ABC is a right angled triangle with ∠C=90
o
,BC=a,AC=b,CD⊥AB and CD=P. Show that
P
2
1
=
a
2
1
+
b
2
1
Medium
Solution
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Given that:
∠C=90
∘
,BC=a,AC=b,CD⊥AB,CD=P
To Prove:
P
2
1
=
a
2
1
+
b
2
1
Solution:
A(ABC)=
2
1
ab=
2
1
P×AB
or, AB=
P
ab
In right angled △ACB,
By Pythagorean theorem,
AB
2
=BC
2
+AC
2
or, (
P
ab
)
2
=a
2
+b
2
or,
P
2
a
2
b
2
=a
2
+b
2
Dividing both sides by a
2
b
2
we get,
or,
P
2
1
=
a
2
1
+
b
2
1
Hence, proved.
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