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Mathematics

Two mutually perpendicular tangents are drawn to a circle with radius R2R\sqrt{2} units. The shortest distance between the two points of contact is :

  1. R units

  2. 12R\dfrac{1}{2}R units

  3. R2R\sqrt{2} units

  4. 2R units

Circles

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Answer

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

Two mutually perpendicular tangents are drawn to a circle with radius R√2 units. The shortest distance between the two points of contact is : Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Given,

Radius = R2R\sqrt{2} units

From figure,

AC = OB = R2R\sqrt{2},

AB = OC = R2R\sqrt{2}.

In right angle triangle ABC,

⇒ BC2 = AB2 + AC2

⇒ BC2 = (R2)2+(R2)2(R\sqrt{2})^2 + (R\sqrt{2})^2

⇒ BC2 = 2R2 + 2R2

⇒ BC2 = 4R2

⇒ BC = 4R2\sqrt{4R^2}

⇒ BC = 2R units.

Hence, Option 4 is the correct option.

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