In an isosceles triangle `A B C` with `A B=A C ,` a circle passing through `B` and `C` intersects the sides `A Ba n dA C` at`Da n dE` respectively. Prove that `DE∣∣BC dot`

Explanation

To prove that line segment DE is parallel to line segment BC in the isosceles triangle ABC where AB = AC and a circle intersects AB and AC at points D and E respectively, we can follow these steps:

### Step-by-Step Solution:

1. **Draw the Triangle and Circle**:
- Start by drawing an isosceles triangle ABC with AB = AC.
- Draw a circle that passes through points B and C, intersecting side AB at point D and side AC at point E.

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