tangents from an external point are equal in length???

  • 0 votes

tangents from an external point are equal in length?

i really dont get that rule?? if someone could slowly explain that rule i would be beyond grateful :)

Posted Tue 10th April, 2012 @ 19:53 by amna

2 Answers

  • 3 votes

(http://www.tutornext.com/system/files/u37/The%20lengths%20of%20tangents%20drawn%20from%20an%20external%20point%20to%20a%20circle%20are%20equal.JPG)

When line PO is drawn, the shape PAOB has been split into two right-angled triangles. These two triangles are identical, so their tangents will be the same. Here is proof that they are the same:

  • The hypotenuse of both PAO and PBO is PO, so they have a identical side.
  • AO=BO, because they are both radii therefore their lengths are the same.
  • Both triangles have a right-angle and two identical sides, this means that the third side will also be the same. Therefore the two tangents will be equal in length.
Answered Wed 11th April, 2012 @ 16:08 by Maleficent
Edited by Maleficent on Wed 11th April, 2012 @ 16:11
  • 0 votes

thank you so much for this, its very clear, and understandable, thank you again! :)

Answered Sat 14th April, 2012 @ 22:11 by amna