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Question
In an equilateral triangle ABC if AD ⊥ BC, then AD2 =
Options
CD2
2CD2
3CD2
4CD2
Solution
In an equilateral ΔABC, `AD ⊥ BC`.
In ΔADC, applying Pythagoras theorem, we get
`AC^2=AD^2+DC^2`
`BC^2=AD^2+DC^2(∵ AC=BC)`
`(2DC)^2=AD^2+DC^2(∵ BC=2DC)`
`4DC^2=AD^2+DC^2`
`3DC^2=AD^2`
Hence, the correct option is (c).
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