In an equilateral triangle `A B C` if `A D_|_B C ,` then `A D^2` = (a)`C D^2` (b) `2C D^2` (c) `3C D^2` (d) `4C D^2`

Explanation

Given, equilateral triangle `ABC, AD⊥BC`

Since, it is an equilaateral triangle, the perpendicualr also bisects the side.

Hence,` BD=DC or BD=(1/2)BC=(1/2)AB`

Now, In` △ABD,` we have

`AB^2=AD^2+BD^2`

`AB^2−BD^2=AD^2`

`BC^2−BD^2=AD^2`

`(2CD)^2−CD^2=AD^2`

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