Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

To find the length of the chord of the larger circle that touches the smaller circle, we can follow these steps:

Step 1: Draw a diagram of the two concentric circles with radii a and b, where a is greater than b.

Step 2: Draw a line segment connecting the center of the larger circle to the point where the smaller circle touches the larger circle. This line segment is the radius of the larger circle and has a length of a.

Step 3: Draw a line segment from the center of the larger circle to the point where the chord touches the larger circle. This line segment is also a radius of the larger circle and has a length of a.

Step 4: Since the chord of the larger circle touches the smaller circle, it is perpendicular to the line segment connecting the centers of the two circles.

Step 5: The line segment connecting the centers of the two circles divides the chord into two equal parts. Let's call the length of each part x.

Step 6: Using the Pythagorean theorem, we can find the length of the line segment connecting the center of the larger circle to the point where the chord touches the larger circle. This length can be expressed as √(a^2 - x^2).

Step 7: Since the line segment connecting the center of the larger circle to the point where the chord touches the larger circle is also a radius of the larger circle, its length is equal to a.

Step 8: Equating the two expressions for the length of the line segment from step 6 and step 7, we have √(a^2 - x^2) = a.

Step 9: Squaring both sides of the equation from step 8, we get a^2 - x^2 = a^2.

Step 10: Simplifying the equation from step 9, we have -x^2 = 0.

Step 11: Solving for x, we find that x = 0.

Step 12: Since x represents the length of each part of the chord, and x cannot be zero, we conclude that the length of the chord of the larger circle that touches the smaller circle is zero.

Therefore, the length of the chord is zero.