So BP is perpendicular to AC and p.

A is AD, and BC is d.

Because AB=AC

So BD= 1/2BC.

Angle ADB=90 degrees

So from the Pythagorean theorem:

AB^2=AD^2+BD^2

Because AB=AC=5 BC=8.

So AD=3

Because the area of the triangle ABC =1/2 * BC * ad =1/2 * AC * BP.

So BP=4.8

So the minimum value of BP is 4.8.