Construction of tanget to a circle and its properties

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)
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
Go back - click here
 * 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.