I hope it doesn't seem like I'm asking a ton of questions, but I'm finishing up my geometry course and I have just a few more questions until I'm completely done!
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hey take help from these
Let AB and AC be two tangent lines from a point A outside a given circle. Show?
that AB is congruent to AC.
How do I write the proof? Please help!
Go to the web site above to see a picture of this problem.
A line which is tangent to a circle at a specific point is perpendicular to a line from the center of the circle to the same point.
The line from the center of the circle to the same point is a radius.
Lines AB and AC are the two tangent lines from a point A outside a given circle.
Let O = center point of the circle.
Lines OB and OC are the radius lines.
The 2 tangent lines, AB and AC, and the 2 radius lines, OB and OC, form a quadrilateral.
Angle ABO and angle ACO are right angles.
A line from the point A to point O divides the quadrilateral into 2 right triangles, ABO and ACO.
Line AO is the hypotenuse of both right triangles.
AB^2 + OB^2 = AO^2
AB^2 = AO^2 – OB^1
AC^2 + OC^2 = AO^2
AC^2 = AO^2 – OC^2
The radius lines, OB and OC, are equal length
So, OB^2 = OC^2.
So, AB = AC