Question

Two mutually perpendicular tangents are drawn to a circle with radius R√2 units. The shortest distance between the two points of contact is:

Options

• R units

• `1/2` R units

• R`sqrt2` units

• 2R units

Answer 1

2R units

Explanation:

Let two perpendicular tangents from external point A touch the circle at points B and C.

Given,

Radius = R`sqrt2` units

From figure,

AC = OB = R`sqrt2`​,

AB = OC = R`sqrt2`

In right angle triangle ABC,

⇒ BC² = AB² + AC²

⇒ BC² = `(R sqrt2)^2 + (R sqrt2)^2`

⇒ BC² = 2R² + 2R²

⇒ BC² = 4R²

⇒ BC = `sqrt(4R^2)`

⇒ BC = 2R units.