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# Construct a $$\triangle{ABC}$$ in which BC = 8 cm, $$\angle{B}$$ = $$45^\circ$$ and AB - AC = 35cm.

Given: In $$\triangle{ABC}$$ in which BC = 8 cm, $$\angle{B}$$ = $$45^\circ$$ and AB - AC = 35cm.
Steps of construction:

1. Draw the base BC = 8cm

2. At the point B make an $$\angle{XBC}$$ = $$45^\circ$$.

3. Cut the line segment BD equal to AB - AC = 3.5 cm from the ray BX.

4. Join DC.

5. Draw the perpendicular bisector, say PQ of DC.

6. Let it intersect BX at a point A.

7. Join AC.
Hence, ABC is the required triangle.