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1- sir is there any relation between secant and tangent of any circle mention it and prove it 2- is it possible that two parallel lines intersect at infinity justify your statement and prove it


1- sir is  there any relation between secant and tangent  of any circle mention it and prove it 


2- is it possible that two parallel lines intersect at  infinity justify your statement  and prove it 


Grade:12

2 Answers

Aman Bansal
592 Points
12 years ago

Dear Keshav,

 If you have a point outside a circle and draw two secant lines (PAB, PCD) from it, there is a relationship between the line segments formed. Refer to the figure above. If you multiply the length of PA by the length of PB, you will get the same result as when you do the same thing to the other secant line.
More formally: When two secant lines AB and CD intersect outside the circle at a point P, then
PA.PB = PC.PD
It is important to get the line segments right. The four segments we are talking about here all start at P, and some overlap each other along part of their length; PA overlaps PB, and PC overlaps PD.
Relationship to Tangent-Secant Theorem
In the figure above, drag point B around the top until it meets point A. The line is now a tangent to the circle, and PA=PB. Since PA=PB, then their product is equal to PA2. So:
PA2 = PC.PD

This is the Tangent-Secant Theorem.

Best Of luck

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Thanks

Aman Bansal

Askiitian Expert


KAMAL RAWAT
39 Points
12 years ago

square(secant)-square(tangent)=1

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