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is a right triangle, right angled at
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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
(i) pc = ab
(ii)
p
2
1
=
a
2
1
+
b
2
1
Easy
Solution
verified
Verified by Toppr
(i) Area of ΔABC=
2
1
BC×AC
=
2
1
×a×b=
2
ab
3
area=
2
1
×CD×AB
2
1
×p×c=
2
pc
2
ab
=
2
pc
ab=pc......(1)
(ii) In ΔABC
AB
2
=AC
2
+BC
2
(
p
ab
)
2
=b
2
+a
2
p
2
1
=
a
2
+b
2
b
2
+a
2
p
2
1
=
a
2
1
+
b
2
1
solution
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SIMILAR QUESTIONS
star-struck
If 8R
2
=a
2
+b
2
+c
2
, then prove that the △ is right angled.
Easy
View solution
>
ABC is a right triangle right angled at C. Let BC=a,CA=b,AB=c and let p be the length of perpendicular from C on AB prove that
i) pc=ab
ii)
p
2
1
=
a
2
1
+
b
2
1
Medium
View solution
>
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