find value of PB-PC
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Intersecting Secants Theorem
When two secant lines intersect each other outside a circle, the products of their segments are equal.
(Note: Each segment is measured from the outside point)
Try this In the figure below, drag the orange dots around to reposition the secant lines. You can see from the calculations that the two products are always the same. (Note: Because the lengths are rounded to one decimal place for clarity, the calculations may come out slightly differently on your calculator.)
See also Intersecting Secant Angles Theorem.
This theorem works like this: 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. by this theorem you can solve it
When two secant lines intersect each other outside a circle, the products of their segments are equal.
(Note: Each segment is measured from the outside point)
Try this In the figure below, drag the orange dots around to reposition the secant lines. You can see from the calculations that the two products are always the same. (Note: Because the lengths are rounded to one decimal place for clarity, the calculations may come out slightly differently on your calculator.)
See also Intersecting Secant Angles Theorem.
This theorem works like this: 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. by this theorem you can solve it
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thank you, can you give me proof of this theorem
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