Two concentric circles of radii a andbwhere a>bare given. The length of thechord of the larger circle whichtouchesthe smaller circle i

The length of the chord of the larger circle which touches the smaller circle can be found using the Pythagorean theorem.

Step 1: Draw a line from the center of the circles to the point where the chord of the larger circle touches the smaller circle. This line is a radius of the larger circle, so its length is 'a'.

Step 2: Draw a line from the center of the circles to the midpoint of the chord. This line is a radius of the smaller circle, so its length is 'b'.

Step 3: The line from step 1, the line from step 2, and the chord form a right triangle. The chord is the hypotenuse of this triangle.

Step 4: Use the Pythagorean theorem to find the length of the chord. The theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, the length of the chord is the square root of (a^2 - b^2).

Step 5: The length of the chord is 2 times the square root of (a^2 - b^2) because the chord is a line segment that passes through the circle and its length is twice the length from the center to the circle along the line of the chord.

So, the length of the chord of the larger circle which touches the smaller circle is 2*sqrt(a^2 - b^2).