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Prove that the tangents drawn to a circle from an external point are congruent. Good luck! cool

 Dec 9, 2018
edited by FreezingTNT  Dec 9, 2018
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Let the external point = C

Let the tangent points be A and B

Let the circle center = 0

 

Draw OC, OA and OB

 

And we have two triangles  OCA  and OCB

 

Now OA and OB are radii drawn to tangent points......so they meet the tangents at right angles

And OA = OB since they are radii

And CO = CO 

 

So....CO is the hypotenuse of two right triangles

And OA and OB are equal legs

 

So...by Hypotenuse - Leg, the other two legs of both triangles - CA and CB - are equal

 

But.....CA and CB are the tangents drawn from C

 

So.....they are equal

 

 

cool cool cool

 Dec 9, 2018
edited by CPhill  Dec 9, 2018

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