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High students in this video, let's continue learning interesting properties about circles over here

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we have a statement.

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The length of two tangents from an exterior point to a circle are equal.

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All right.

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Let's try to understand this.

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Over here you have a circle and point is an exterior point to the circle.

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And the two tangents are A, B and C.

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And over here, it's mentioned that the length will be equal, that is about equal to is it?

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All right.

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Can you tell me why that is?

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So let's try to think about it together again.

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We brought this with congruency of triangles.

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Let all be the center of the circle.

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Let me join.

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Or B or C and or A.

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All right, now let's try to analyze Triangle A or B and Triangle E or C. All right.

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In these two triangles, you can see that all be will be equal to Ossy, right?

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Y because both of them are really right.

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The radius of a circle is constant.

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So Albe is equal to O.C. Now all M is a common sight.

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Right.

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So all it is equal in both these triangles.

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Now is there anything else that you know about this case?

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Yes, it's given that these two are tangents engines.

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Right.

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And we know that if you have a tangent and at the point of intersection of the tangent with the circle,

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if you joined that to the center of the circle, the angles all formed will be a right angle to this

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angle.

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Over here is 90 degree and this angle over here is 90 degrees.

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So Angle or B is equal to angle or C is equal to 90 degrees.

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Therefore, we have A right to right angles.

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We have the hypotenuse is equal and we have one set of sides equal, therefore espera, which is congruency

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rule.

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These two triangles are congruent.

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Right.

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So if these two triangles are congruent, then you can find that Ebbie is equal to AC because these

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are corresponding sides of two congruent triangles.

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Therefore, if you have an exterior point and if you draw tangent to a circle from that extra point,

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then the length of those tangents, that is the length from the point from where the tangent is drawn

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to the point where the tangent intersects the circle, those two lengths will be equal or in the diagram

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abs equal to AC.