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

FreezingTNT Dec 9, 2018

#1**+1 **

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

CPhill Dec 9, 2018