D and E are mid points of sides AB and AC respectively of the triangle ABC. A line drawn from A meets BC and H and DE at K. What is AK: KH?

Question

D and E are mid points of sides AB and AC respectively of the triangle ABC. A line drawn from A meets BC and H and DE at K. What is AK: KH?

1) $1:1$

2)$2:1$

3) $1:3$

4) $1:2$

Efforts:

By Thales Theorem, DE is parallel to BC. Now how should I proceed from here??

Thanks.

Answer 1

With ED || BC, identify similar triangles ADK and ABH to obtain

AK : AH = AD : AB = 1 : 2.

Then, AK : KH = 1 : 1.