`ABC` is a right triangle with `AB` = `AC`.If bisector of `angle A ` meet `BC` at `D` then prove that `BC` =`2` `AD` .

Explanation

To prove that \( BC = 2 \cdot AD \) in triangle \( ABC \) where \( AB = AC \) and \( \angle A = 90^\circ \), we can follow these steps:

### Step 1: Understand the triangle configuration
Since \( ABC \) is a right triangle with \( AB = AC \), it is an isosceles right triangle. This means that \( \angle B = \angle C = 45^\circ \).

### Step 2: Identify the angle bisector
Let \( AD \) be the angle bisector of \( \angle A \). Since \( \angle A = 90^\circ \), the angle bisector \( AD \) divides \( \angle A \) into two equal angles:
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