PeterWhite

It is Very easy : The angle PAC=25 and it is subtended at the circumference and its sides define the arc PC and the chord PC.This angle ,according to a well known theorem of Euclidean Geometry is equal to the angle formed by the chord PC and the Tangent to the circle at C. since the angle DCP is 25 degrees it follows that the line PC is tangent to the circle at C.

As simple as such.

MINOAS