Question

What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

Answer 1

In the given figure, O is the centre of the circle. Line PT and line QR are two parallel tangents to the circle at P and Q, respectively.

∴ ∠OPT + ∠OQR = 180º (Sum of adjacent interior angles on the same side of the transversal is supplementary)

⇒ POQ is a straight line segment.

∴ PQ is the diameter of the circle.

PQ = Distance between the parallel tangents PT and QR = 2 × Radius = 2 × 4.5 = 9 cm

Thus, the distance between two parallel tangents of the circle is 9 cm.