The radii of two concentric circles are 26 cm and 10 cm. If a chord of the greater circle is tangent to the smaller circle, find the length of that chord.

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Given two concentric circles with radii 26 cm (greater circle) and 10 cm (smaller circle). A chord of the greater circle is tangent to the smaller circle.

Step 1: Since the circles are concentric, their centers coincide. Let the center be O.

Step 2: The chord of the greater circle is tangent to the smaller circle. This means the shortest distance from the center O to the chord equals the radius of the smaller circle (10 cm).

Step 3: Let the chord length be 2x. The distance from the center to the chord is the perpendicular from O to the chord.

Step 4: In the greater circle, radius = 26 cm. The perpendicular distance from center to chord = 10 cm.

Step 5: Using the right triangle formed by the radius, half chord, and perpendicular distance:

(half chord)^2 + (distance from center to chord)^2 = (radius of greater circle)^2

x^2 + 10^2 = 26^2

x^2 + 100 = 676

x^2 = 676 - 100 = 576

x = sqrt(576) = 24 cm

Step 6: Length of chord = 2x = 2 * 24 = 48 cm

Therefore, the length of the chord is 48 cm.

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