Tangents to a circle

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Objectives

To understand about the tangent and its relationship to the circle

Estimated Time

30 minutes

Prerequisites/Instructions, prior preparations, if any

Knowledge about Circle, radius, angle

Materials/ Resources needed

Digital: Click here to open the file

Non-digital:Paper, pencil, ruler, compass, protractor.

Process (How to do the activity)


Download this geogebra file from this link.


Procedure:

  1. 'A' is the center of the circle
  2. What are 'AD' and 'AE' with respect to the circle?
  3. What type of angles are ∠BDA and ∠BEA ?
  4. In any circle the radius drawn at the point of contact is perpendicular to the tangent. ∠BDA = ∠BEA = 90
  5. We can draw two tangents to a circle from a point outside the circle
  6. Name the tangents drawn from the external point B to the circle
  7. Measure AD and AE. What is your conclusions?
  8. What type of triangles are BDA and BEA ?
  9. What is AB with respect to triangle BDA and BEA ?
  10. Are triangle BDA and BEA congruent to each other?
  11. The tangent drawn from an external point to a circle a] are equal b] subtend equal angle at the centre c] are equally inclined to the line joining the centre and external point.
  12. Properties of quadrilateral (sum of all angles) is 360 degrees
  13. Angle between the two tangents from a point outside the circle is supplementary to the angle subtended by the line segments joining points of contact at the centre.

Evaluation at the end of activity

Tangents AP and AQ are drawn to circle with centre 'O', from an external point 'A'.Prove that ∠PAQ=2∠OPQ

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