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Question
If ∆ABC is an equilateral triangle such that AD ⊥ BC, then AD2 =
Options
- \[\frac{3}{2} {DC}^2\]
2 DC2
3 CD2
4 DC2
Solution
Given: In an equilateral ΔABC, `AD ⊥ BC`.
Since `AD ⊥ BC`., BD = CD = \[\frac{BC}{2}\]
Applying Pythagoras theorem,
In ΔADC
`AC^2+AD^2+DC^2`
`BC^2=AD^2+DC^2`(Since AC=BC)
`(2DC)^2=AD^2+DC^2`(Since BC=2DC)
`4DC^2=AD^2+DC^2`
`3DC^2=AD^2`
`3DC^2=AD^2`
We got the result as `c`
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