Question

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

Answer 1

⇒ O is the center of the circle.

⇒ l and m are two parallel tangents of the circle.

⇒ Radius of the circle =4.5cm

⇒ AB is distance between two parallel tangents.

⇒ AB=OA+OB=4.5cm+4.5cm

∴ AB=9cm

∴ Distance between the parallel tangents l and m is 9cm.

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Answer 2

Step-by-step explanation:

Let the lines PQ and RS be the two parallel tangents to circle at M and N respectively. Through centre O, draw line AB || line RS.

OM = ON = 4.5 [Given]

line AB || line RS [Construction]

line PQ || line RS [Given]

∴ line AB || line PQ || line RS

Now, ∠OMP = ∠ONR = 90° (i) [Tangent theorem]

For line PQ || line AB,

∠OMP = ∠AON = 90° (ii) [Corresponding angles and from (i)]

For line RS || line AB, ∠ONR = ∠AOM = 90° (iii) [Corresponding angles and from (i)]

∠AON + ∠AOM = 90° + 90° [From (ii) and (iii)]

∠AON + ∠AOM = 180°

∠AON and ∠AOM form a linear pair.

ray OM and ray ON are opposite rays.

Points M, O, N are collinear. (iv)

MN = OM + ON [M – O – N, From (iv)]

MN = 4.5 + 4.5

MN = 9 cm

Distance between two parallel tangents PQ and RS is 9 cm.

So, ur Answer is 9cm.