Two direct common tangents are drawn to two non-intersecting circles.prove that the segments between the points of contact are equal.

Answer :

We form our diagram from given information , As :

Here Point of contact of two direct chords is A , B  and C , D .

We know " A tangent to a circle is perpendicular to the radius at the point of tangency. " 

And we join center of  "  M  "  to tangents that meet at A and D  , and another circle with center " N "  to tangent that meet at "  B  "  and "  C " .

So,

MAB  = 90°  ,

MDC  = 90°
And
NBA  = 90° ,
NCD  = 90°

SO,
In quadrilateral ABCD , all four angles are at 90° , So ABCD is a rectangle .

And We know opposite side of rectangle are equal to each other . 

So,

AB =  CD                                                                                  ( Hence proved )

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