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Magazine Problem 355
Prove that the measure of the angle formed by a tangent and a chord of a circle is one-half the measure of its intercepted arc.
Problem 357
The angle formed by two tangents drawn to a circle from the same external point measures \(80^{\circ}\). Find the measure of the minor intercepted arc.
Problem 366
Two secant lines of the same circle share an endpoint in the exterior of the circle. Show that the product of the lengths of one secant segment and its external segment equal the product of the lengths of the other secant segment and its external segment.
Problem 367
\(\underline{P B}\) and \(\underline{P D}\), which are secants drawn to circle \(O\), intersect the circle in points \(A\) and \(C\), respectively. In the figure shown, if \(\mathrm{PA}=4, \mathrm{AB}=5\), and \(\mathrm{PD}=12\), find \(\mathrm{PC}\)
Problem 371
Prove: Whether an angle that is exterior to the circle is formed by two secants to the circle, a secant and a tangent to the circle, or two tangents to the circle, the measure of the angle equals the difference in the measures of the intercepted arcs.
