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Diagram

Draw a circle with center O and radius 3.6 cm. Draw a tangent to the circle from point B at a distance of 7.2 cm from the center of the circle.

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#### Solution

**Analysis:**

As shown in the figure, let B be a point in the exterior of the circle at a distance of 7.2 cm from O.

Let BR be the tangent to the circle at points R.

∴ seg OR ⊥ tangent BR ......[Tangent theorem]

∴ ∠ORB = 90°

∴ Point R is on the circle having OB as diameter. ......[Angle inscribed in a semicircle is a right angle]

On drawing a circle with OB as diameter, the point where it intersects the circle with centre O, will be the position of point R.**Steps of construction:**

- With centre O, draw a circle of radius 3.6 cm
- Take point B such that OB = 7.2 cm
- Draw the perpendicular bisector of seg OB. It intersects OB in point M.
- With M as centre and radius equal to OM, draw an arc intersecting the circle in points R.
- Draw ray BR.

Ray BR is the required tangent to the circle.

Concept: Construction of a Tangent to the Circle at a Point on the Circle

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