00:01
We want to prove the segments and segments of sequence and tangents theorem.
00:06
And this time we're going to do it with a two column prove.
00:09
Let's first draw a diagram for reference.
00:12
So we have a circle and the tangents and sequence of sequence theorem.
00:23
So sequence of segments of sequence and tangents theorem says that if we have a tangent, let's call it e .a.
00:44
And a secant segment, so it hits the circle in two locations.
00:53
Let's call it c .d.
00:58
Then we want to prove that the tangent ea squared would be equal to the external secant segment ec times the entire secant ed that's what we would want to prove from this picture so we're going to do this two column and we are given the picture that ea segment ea is a tangent and that segment ed is a secant segment now let's add to the picture ac and ad we would know that angle e if we're thinking about two different triangles triangle e a c and triangle ead we would know that angle e is congruent to itself that's the reflexive property then we would know that the measure of angle e a c let me just highlight it here.
02:50
This angle eac would be half of arc ac because angle eac is inscribed opening up to arc ac.
03:01
So the angle is half of the arc measure.
03:06
So let me say that again.
03:08
The measure of angle eac would be half of the measure of arc ac.
03:18
That's called the tangent and intersected chord theorem.
03:39
From the text, this is theorem 2 .2.
03:43
From the text, this is theorem 10 .14.
03:48
Now we also know that the measure of angle adc opens up to the same arc ac, and by the same reason, angle adc has to be half of the measure of arc ac...