# Construction of tanget to a circle and its properties

## Contents

### Objectives

Understand the construction of Tangents from an external point and its properties.

### Estimated Time

40 minutes

### Prerequisites/Instructions, prior preparations, if any

Knowledge about radius, perpendicular bisector, tangents

### 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:**

- Draw a circle with centre 'O' and radius and take a point 'P' away from the centre and join OP.
- Draw the perpendicular bisector of OP and mark the mid point of OP as C.
- With CO or CP as radius draw a circle to intersect the circle already drawn mark and name the intersecting points Q and R.
- Join PQ and PR. PQ and PR are the required tangents.
- Measure PQ and PR. What is your conclusions?
- Length of tangents from an external point are equal i.e. length of tangent PQ is equal to length of tangent PR
- Join OQ and OR, find angles QPR and ROQ.
- Sum of the angle at the centre of circle and at external point is supplementary. Sum of opposite angles=180°
- Move slider or point P to verify the properties

### Evaluation at the end of the activity

- Construct a circle of radius 6 cm and construct tangents to it from an external point 10 cm away from the centre. Measure and verify the length of the tangents.
- Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the circle.

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