If the radii of two concentric circles are 4 cm and 5 cm, then the length of a chord of one circle that is tangent to the other circle is

Two concentric circles have radii $4$ cm and $5$ cm. The chord of the outer circle is tangent to the inner circle.

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When a chord is tangent to a circle, the perpendicular distance from the center to the chord equals the radius of that circle.

Distance from center $O$ to chord $AB = 4$ cm

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Let $M$ be the point where the chord touches the inner circle. In right triangle $OMA$:

$OM = 4$ cm (perpendicular distance)

$OA = 5$ cm (radius of outer circle)

Using Pythagorean theorem:

$OA^2 = OM^2 + AM^2$

$5^2 = 4^2 + AM^2$

$25 = 16 + AM^2$

$AM^2 = 9$

$AM = 3$ cm

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Since the perpendicular from center bisects the chord:

$AM = MB = 3$ cm

Chord length:

$AB = AM + MB$

$AB = 3 + 3$

$AB = 6$ cm

Therefore, the chord length is $6$ cm.