# Construction of tanget to a circle and its properties

### Objectives

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

40 minutes

### Materials/ Resources needed

Non-Digital : paper, pencil, ruler, compass, protractor

### Process (How to do the activity)

Procedure:

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

### Evaluation at the end of the activity

1. 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.
2. Construct a pair of tangents to a circle of radius 3.5 cm from a point 3.5 cm away from the circle.