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. - Geometry Mathematics 2

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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:

  1. With centre O, draw a circle of radius 3.6 cm
  2. Take point B such that OB = 7.2 cm
  3. Draw the perpendicular bisector of seg OB. It intersects OB in point M.
  4. With M as centre and radius equal to OM, draw an arc intersecting the circle in points R.
  5. Draw ray BR.
    Ray BR is the required tangent to the circle.
  Is there an error in this question or solution?
Chapter 4: Geometric Constructions - Q.3 (B)

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