In two concentric circle, prove that a chord of larger circle which is tangent to smaller circle is bisected at the point of contact.

Explanation

Assume, `O` be the common centre of two concentric circles, and Assume A B be a chord of the larger circle touching the smaller circle at P.


prove: AB is bisected at P.


Join OP


As OP is the radius of the smaller circle and AB is a tangent to this circle at a point P.


So, ` OP bot AB`


Given: the perpendicular drawn from the centre of a circle to any chord of the circle, bisects the chord.


So, `O P bot A B`


`Rightarrow AP = BP`


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