With O as a center and a radius of about 1 inch draw the given circle. Assume P some point outside of the circle about 2 1/2 inches from the center. Draw a straight line passing through P and O. Bisect P O and with the middle point F as a center describe the circle passing through P and 0. Draw a line from P through the intersection of the two circumferences C. The line P C is tangent to the given circle. S nilarly P E is tangent to the circle.
The angle P C O is inscribed in a semicircle and hence is a right angle. Since P C 0 is a right angle, P C is perpendicular to C 0. The perpendicular to a radius at its extremity is tangent to the circumference.