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.