Difference between revisions of "Tangents to a circle"

Latest revision as of 14:03, 19 December 2020

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 open the file

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

Process (How to do the activity)

Download this geogebra file from this link.

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 - click here

@@ Line 1: / Line 1: @@
 ===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===
 minutes
 ===Prerequisites/Instructions, prior preparations, if any===
+Knowledge about Circle, radius, angle
 ===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
+Non-digital:Paper, pencil, ruler, compass, protractor.
 ===Process (How to do the activity)===
@@ Line 12: / Line 16: @@
 '''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.
+# Measure AD and AE. What is your conclusions?
-## 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 isoscles triangle.
+# What is AB with respect to triangle 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]]