View source for Tangents to a circle

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

Non-digital:Paper, pencil, ruler, compass, protractor.

===Process (How to do the activity)===
{{Geogebra|tk7wbpwe}}

'''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

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