A line through the variable point `A(k+1,2k)` meets the lines `7x+y-16=0,5x-y-8=0,x-5y+8=0` at `B ,C ,D ,` respectively. Prove that `A C ,A B ,A D` are in HP.

Explanation

To prove that the distances \( AC, AB, AD \) are in Harmonic Progression (HP), we will follow these steps:

### Step 1: Identify the coordinates of point A
The coordinates of point A are given as:
\[ A(k+1, 2k) \]

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