Changes

===Objectives===

===Objectives===

To understand what is a tangent and its relationship to the circle

To understand about the tangent and its relationship to the circle

===Estimated Time===

===Estimated Time===

30 minutes

30 minutes

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

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

===Materials/ Resources needed===

===Materials/ Resources needed===

Click here to [https://karnatakaeducation.org.in/KOER/en/images/2/2b/TANGENTS_TO_A_CIRCLE.ggb open] the file

Digital: Click here to [https://karnatakaeducation.org.in/KOER/en/images/2/2b/TANGENTS_TO_A_CIRCLE.ggb open] the file

 

===Process (How to do the activity)===

===Process (How to do the activity)===

'''Procedure:'''

'''Procedure:'''

# O is the center of the circle and tangents AP and AQ are drawn from an external point A.

# 'A' is the center of the circle

# OP and OQ are the radii.

# What are 'AD' and 'AE' with respect to the circle?

# The radii of a circle are equal.

# 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

# 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

# We can draw two tangents to a circle from a point outside the circle

## The lengths of the tangents from a point to a circle are equal BD=BE

# Name the tangents drawn from the external point B to the circle

## 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 extrnal point.

## Angle between the two tangents from a point outside the circle is supplementary to the angle subtended  by the line segmnets joining points of contact at the cente

# What type of triangles are BDA and BEA ?

## Properties of quadrillateral ( sum of all angles) is 360 degrees

# Are triangle BDA and BEA congruent to each other?

## Sum of three angles of triangle is 180 degrees.

# 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

Go back - [https://karnatakaeducation.org.in/KOER/en/index.php/KVS_Circles#Tangents_to_a_Circle click here]

Go back - [https://karnatakaeducation.org.in/KOER/en/index.php/Circles?veaction=edit&section=42 click here]

[[Category:Circles]]

[[Category:Circles]]