# Tangents to a circle

### Objectives

To understand about the tangent and its relationship to the circle

30 minutes

### Materials/ Resources needed

Digital: Click here to open the file

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

### Process (How to do the activity)

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