from units TRIANGLES

Draw the diagram as mentioned in the question.

Let CD be theperpendicular from C to AB.

Acc to question,

AB=c,BC=a, AB=c,CD=p

CAB is a right triangle and so is DCB.

angle BDC= angle BCA( each is 90 )

angle DBC= angle ABC(common angle to both triangles)

So,

 triangle DCB similar to triangle CAB(AA rule)

DC/CA=CB/AB( corr sides of similar trianglesaa re proportional)

p/b=a/c

1/p=c/ab

squaring both sides,

solving one step further we get the answer.