Question

In an equilateral triangle ABC if AD ⊥ BC, then AD² =

Options

•  CD²

• 2CD²

• 3CD²

• 4CD²

Answer 1

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).