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Draw a circle of diameter 6.4 cm. Take a point R at a distance equal to its diameter from the center. Draw tangents form point R.

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Diameter of circle = 6.4 cm 6.4 

Radius of circle = 6.4/2 = 3.2 cm 

Analysis: 

As shown in the figure, let R be a point in the exterior of circle at a distance of 6.4 cm. 

Let RQ and RS be the tangents to the circle at points Q and S respectively.

          Rough Figure 

∴ seg PQ ⊥tangent RQ …[Tangent is perpendicular to radius] 

∴ ∠PQR = 90° 

∴ point Q is on the circle having PR as diameter. …[Angle inscribed in a semicircle is a right angle] 

Similarly, Point S also lies on the circle having PR as diameter. 

∴ Points Q and S lie on the circle with PR as diameter. 

On drawing a circle with PR as diameter, the points where it intersects the circle with centre P, will be the positions of points Q and S respectively.

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