in two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal lengths.
let AB be the chord of outer circle and OM be the radius of the inner circle which touches the chord AB.
to prove ---
AM = BM
OM is perpendicular to AB.
in triangle OMB and triangle OMA,
OM = OM [ common ]
OB = OA [ radius of outer circle. ]
<OMB = <OMA
tri. OMA ia congruent to tri. OMB .[ SAS rule ]
MB = MA [ cpct ]
HOPE THIS HELPS...