In two concentric circles, prove that all chords of the outer circle which touch the inner circle, are of equal length.
Given
and chords of outer circle tangent to the inner circle.
common centre of and and are points of contact of
To Prove
Theorem Tangent at any point of the circle is perpendicular to the radius through the point of contact
According to the above theorem
and
Now in
( Radius of )
( Radius of )
(from (i))
Now using R.H.S congruency rule
This means
Similarly and are congruent
Adding (i) and (iii)
Hence Proved