SOLUTION: . If two circles are concentric and a chord of the larger circle is tangent to the smaller circle, prove that the point of tangency is the midpoint of the chord.

Question 983406: . If two circles are concentric and a chord of the larger circle is tangent to the smaller circle, prove that the point of tangency is the midpoint of the chord.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

.

For the smaller circle AC is the tangent at point B
Therefore AB is perpendicular to AC. ( Tangent -radius)
Now for the larger circle AC is the chord and OB is perpendicular to AC at B.
therefore AB = BC . ( A line drawn perpendicular to a chord from the centre bisects the chord)
Therefor B is the mid point AC the chord.

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