Question

In triangle ABD, C is the point on BD such that BC : CD = 1:2 and triangle ABC is an equilateral triangle. Prove that AD^2 = 7AC^2

Answer 1

Answer:

hope it helps u

Step-by-step explanation:

as been attached

@supriya789

Answer 2

Answer:

Step-by-step explanation:

Given: In triangle ABD, C is the point on BD such that BC : CD = 1:2 and triangle ABC is an equilateral triangle.

To Prove: AD^2 = 7AC^2

Solution:

    In △ABD, BC : CD = 1 : 2

   In △ABC, AB = BC = CA

Draw AE⊥BC

In △ABC,

                      BE = EC = a/2 and

                      AE = a√3/2

      In △ADE, ∠AED=90°  [∵ Construction]

  ∴   AD² = AE² + ED²     [∵ Pythagoras theorem]

AD² = (a√3/2)² + (2a + a/2)²

AD² = 3a²/4 + 25a²/4

AD² = 28a²/4

AD² = 7a²

AD² = 7AC²

Hence, proved AD² = 7AC²

                                                       #SPJ3