A triangle is right angled at b and e are points on bc trisect it,if ab=8cm,bc=6cm then
a)ae^2=80
b)AC^2=100
c)AD^2=68
d)8AE^2=3AC^2-5AD^2
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In right angled Triangle ABC if D and E trisect BC then prove that 8AE
2
=3AC
2
+5AD
2
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ANSWER
Since D and E are the points of trisection of BC therefore BD=DE=CE
Let BD=DE=CE=x.
Then BE=2x and BC=3x
In rt △ABD,
AD
2
=AB
2
+BD
2
=AB
2
+x
2
(i)
In rt △ABE,
AE
2
=AB
2
+BE
2
=AB
2
+4x
2
(ii)
In rt △ABC,
AC
2
=AB
2
+BC
2
=AB
2
+9x
2
(iii)
Now, 8AE
2
−3AC
2
−5AD
2
=8(AB
2
+4x
2
)−3(AB
2
+9x
2
)−5(AB
2
+x
2
)
=0
Therefore, 8AE
2
=3AC
2
+5AD
2
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