Grade 12Analytical Geometry

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

keshav kr

14 Years agoGrade 12

2 Answers

Aman Bansal

14 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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Aman Bansal

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