If the median AM , angle bisector AD and altitude AH drawn from vertex A of a triangle ABC divide angle A into four equal (D lying between H and M) , then

Options

A. `A=pi/3`
B. `A=pi/2`
C. `(AC)/(AB)=sqrt2+1`
D. `(AC)/(AB)=1/(sqrt2+1)`

Explanation

To solve the problem, we need to analyze the triangle ABC with the given conditions.

### Step-by-Step Solution:

1. **Understanding the Problem**: We have a triangle ABC where the median AM, angle bisector AD, and altitude AH from vertex A divide angle A into four equal parts. Let each of these parts be denoted as \( \theta \). Therefore, we can express angle A as:
\[ \angle A = 4\theta \]
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