Day eight : The tangent and Secant line in a circle

by Nami Youn


Objective

To discover the relationship of Tangent line and Secant line of a circle


Property 1

From a point outside a circle, construct the tangent and secant line.Let the intersection point of the tangent and the circle be T. Let the intersection points of the secant and the circle be A and B. Then, PT PT =PAPB
If the points A and B lie on the half line with point P as an endpoint and point T does not lie on this half line, PT PT =PAPB, then the line PT is a tangent line of this circle passing through A, B, and T.
 
 






gsp file
 



2. Extension

Isosceles triangle
 
 

 ABAB =ACAC=APAQ
 
 


 
 







gsp file


The common tangent line of two circles
 
 


PAPB = PCPD
 
 
 
 
 
 


 
 
 
 



Let the intersection point of extension lines of two chords AB and CD in a circle be P. If PAPB = PCPD, then the four points A, B, C, and D lie on a circle.
 
 

gsp file



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