High students in this video, let's continue learning interesting properties about circles over here
we have a statement.
The length of two tangents from an exterior point to a circle are equal.
All right.
Let's try to understand this.
Over here you have a circle and point is an exterior point to the circle.
And the two tangents are A, B and C.
And over here, it's mentioned that the length will be equal, that is about equal to is it?
All right.
Can you tell me why that is?
So let's try to think about it together again.
We brought this with congruency of triangles.
Let all be the center of the circle.
Let me join.
Or B or C and or A.
All right, now let's try to analyze Triangle A or B and Triangle E or C. All right.
In these two triangles, you can see that all be will be equal to Ossy, right?
Y because both of them are really right.
The radius of a circle is constant.
So Albe is equal to O.C. Now all M is a common sight.
Right.
So all it is equal in both these triangles.
Now is there anything else that you know about this case?
Yes, it's given that these two are tangents engines.
Right.
And we know that if you have a tangent and at the point of intersection of the tangent with the circle,
if you joined that to the center of the circle, the angles all formed will be a right angle to this
angle.
Over here is 90 degree and this angle over here is 90 degrees.
So Angle or B is equal to angle or C is equal to 90 degrees.
Therefore, we have A right to right angles.
We have the hypotenuse is equal and we have one set of sides equal, therefore espera, which is congruency
rule.
These two triangles are congruent.
Right.
So if these two triangles are congruent, then you can find that Ebbie is equal to AC because these
are corresponding sides of two congruent triangles.
Therefore, if you have an exterior point and if you draw tangent to a circle from that extra point,
then the length of those tangents, that is the length from the point from where the tangent is drawn
to the point where the tangent intersects the circle, those two lengths will be equal or in the diagram
abs equal to AC.