MathNet 2015-part-01 — 191 problems (EN–VI) Question 177

a) The Equal Tangents Theorem (called the "Teorema do Bico" in Brazil) says that the distances from a point outside a circle to the points where its tangents touch the circle are equal. In the following figure, $AP$ and $AQ$ are tangent to the circle. Show that $AP = AQ$.



b) Consider the hexagon in the following figure, in which all sides are tangent to the circle. Determine the value of the unknown side $x$.