# 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:**

- 'A' is the center of the circle
- What are 'AD' and 'AE' with respect to the circle?
- What type of angles are ∠BDA and ∠BEA ?
- In any circle the radius drawn at the point of contact is perpendicular to the tangent. ∠BDA = ∠BEA = 90
- We can draw two tangents to a circle from a point outside the circle
- Name the tangents drawn from the external point B to the circle
- Measure AD and AE. What is your conclusions?
- What type of triangles are BDA and BEA ?
- What is AB with respect to triangle BDA and BEA ?
- Are triangle BDA and BEA congruent to each other?
- 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.
- Properties of quadrilateral (sum of all angles) is 360 degrees
- 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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