Students in this video, let's discuss an important theorem which is very useful in solving a lot of
questions called the second tangent theorem.
Over here I have a circle with center O and a B is a second.
OK, so it's interesting, the circle at two points and B and L is a tangent at point B now as per the
second tangent theorem, angle A, B, B, that is this angle over here will be equal to the angle SUB-STANDARD
baby that's angle HCB.
Or here to ask for this theorem angle B is equal to angle HCB.
All right, now over here, you can note that this angle over here is the angle between the second and
the tangent, you have the second over here and the tangent over here.
But this is the angle between the second and the tangent.
Now, let's try to understand why this is true.
Let's join in with all and all will be all right.
Now, these two angles will be equal because or and or B are equal.
Right.
So it is an isosceles triangle now as angle HCB.
That's this angle over here is theta.
Therefore we can find that angle A or B will be equal to two Tetum.
Right.
Because Angle AOB is the measure of archabbey and angle.
ACB is an angle sub-standard by the same arc and we have seen that the angle SUB-STANDARD will be half
the measure.
Right, or the measure will be twice the SUB-STANDARD angle.
So AOB is equal to Tetum already.
Now let's observe isosceles triangle.
It will be we have angle y angle.
Right and this angle over here will be to teeter right.
Therefore we can find that angle y will be 180 minus two feet by two.
That's equal to 90 minus to.
All right.
Now angle all BP will be equal to 90 degree.
Right, because it is a tangent.
OK, so now let's find angle B B, that's what we are trying to find, right?
This is data and we are trying to prove that angle.
Pibor also is equal to data.
All right.
So angle B B will be equal to 90.
That's this angle over here, minus Y, right.
If you subtract from this angle y, you are left with only this much and that is angle PVA.
That's 90 minus Y and we know Y is equal to 90 minus theta will be substituted over here.
So we get ninety minus 90 plus theta which is equal to Tweetup.
So angle B B, A is equal to Peter.