MCQ
In an equilateral triangle ABC if $\text{AD}\perp\text{BC},$ then $AD^2 =$
- A$CD^2$
- B$2CD^2$
- ✓$3CD^2$
- D$4CD^2$
✓
Answer
Correct option: C.
$3CD^2$
In an equilateral $\triangle\text{ABC},\ \text{AD}\perp\text{BC}$
In $\triangle\text{ADC},$ applying Pythagoras theorem, we get,
$AC^2 = AD^2 + DC^2$
$BC^2 = AD^2 + DC^2 (\because AC = BC)$
$(2DC)^2 = AD^2 + DC^2 (\because BC = 2DC)$
$4DC^2 = AD^2 + DC^2$
$3DC^2 = AD^2$
$3CD^2 = AD^2$
Hence, the correct option is $C$.
In $\triangle\text{ADC},$ applying Pythagoras theorem, we get,
$AC^2 = AD^2 + DC^2$
$BC^2 = AD^2 + DC^2 (\because AC = BC)$
$(2DC)^2 = AD^2 + DC^2 (\because BC = 2DC)$
$4DC^2 = AD^2 + DC^2$
$3DC^2 = AD^2$
$3CD^2 = AD^2$
Hence, the correct option is $C$.
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