Fill in the blanks.

(i) A line intersecting a circle in two distinct points is called a ……..

(ii) A circle can have ………..parallel tangents at the most.

(iii) The common point of a tangent to a circle and the circle is called the ………..

(iv) A circle can have ………..tangents.

In the given figure, PA and PB are two tangents from an external point P to a circle with center O. If ∠PBA = 65°, find ∠OAB and ∠APB.

Two tangent segments BC and BD are drawn to a circle with center O such that ∠CBD = 120°. Prove that OB = 2BC.

Prove that the lengths of two tangents drawn from an external point to a circle are equal.

Prove that the tangents drawn at the ends of the diameter of a circle are parallel.