In angle ABC,B = 90° AB=AC Prove that D is the mid point of AC
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In ΔABC,
AB
2
+BC
2
=AC
2
as [BC=2CD]
AB
2
+4CD
2
=AC
2
--(1)
In ΔABD,
AD
2
=AB
2
+BD
2
=AB
2
+CD
2
--(2)
Subtracting (1) and (2)
AC
2
−AD
2
=AB
2
+4CD
2
−(AB
2
+CD
2
)
AC
2
−AD
2
=3CD
2
AC
2
=AD
2
+3CD
2
Hence proved.
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