If A B C is an equilateral triangle such that A D ⊥ B C, then A D^2= (a) 3/2 D C^2 (b) 2 D C^2 (c...

If A B C is an equilateral triangle such that A D ⊥ B C, then A D^2=
(a) 3/2 D C^2
(b) 2 D C^2
(c) 3 C D^2
(d) 4 D C^2

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Given, equilateral triangle ABC, AD⊥BC
Since, it is an equilaateral triangle, the perpendicualr also bisects the side.
Hence, BD=DC or BD=
2
1
​
BC=
2
1
​
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

⇒3CD
2
=AD
2