In Figure, AD ,BC and BD=CD. Prove that 2CAP=2AB2-BC?.
А
B
D
Answers
Answered by
1
Answer:
Given ABC is a triangle and AD⊥BC.
To prove : 2CA
2
−2.AB
2
+BC
2
proof : BD+CD=BC
3
1
.CD+CD=BC
CD+3CD=3.BC
4CD=3BC
CD=
4
3
.BC⋯(1)
From (1)
BD=
4
3
.BC
BD=
4
BC
⋯(2)
In △ACD,
AC
2
=AD
2
+DC
2
⋯(3)
In △ADB,
AB
2
=AD
2
+BD
2
AD
2
=AB
2
−BD
2
⋯(4)
put (4) in (1)
AC
2
=AB
2
−BD
2
+DC
2
AC
2
=AB
2
−(
4
BC
)
2
+(
4
3
.BC)
2
AC
2
=AB
2
−
16
BC
2
+
16
9.BC
2
AC
2
=AB
2
+
16
−BC
2
+9BC
2
AC
2
=AB
2
+
16
8.BC
2
AC
2
=AC
2
=
2
2.AB
2
+BC
2
∴2AC
2
=2AB
2
+BC
2
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