What will be the distance between two parallel tangents of a circle of radius 5cm

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.

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠ POQ = 110°, then ∠ PTQ is equal to(A) 60° (B) 70°(C) 80° (D) 90°

Fig. 10.11

It is given that,∠POQ =110°Since, the Iangent at any point of a circle is perpendicular to the radius through the point of contact.∴ ∠OPT = 90°and ∠OQT = 90°Now, in quadrilateral POQT.∠POQ + ∠OQT + ∠PTQ + ∠OPT = 360°(angle sum property of quadrilateral)⇒110° + 90° + ∠PTQ + 90° = 360°⇒ ∠PTQ + 290° = 360°⇒ ∠PTQ = 70°

Hence, right option is (B).

What the distance between two parallel tangents to a circle of radius 5 cm?

Question:

What the distance between two parallel tangents to a circle of radius 5 cm?

Solution:

Two parallel tangents can exist at the two ends of the diameter of the circle. Therefore, the distance between the two parallel tangents will be equal to the diameter of the circle. In the problem the radius of the circle is given as 5 cm. Therefore,

Diameter = 5 × 2

Diameter = 10 cm

Hence, the distance between the two parallel tangents is 10 cm.

What the distance between two parallel tangents to a circle of radius 5 cm ?

Solution