Final answer:
To find the length of the chord of the larger circle which touches the smaller circle, we can use the property that the angle between a tangent and a chord drawn from the point of contact is 90 degrees. Using this property, we can draw a line connecting the centers of the two circles, and it will be perpendicular to the chord. We can use the Pythagorean theorem to find the length of the line connecting the centers of the circles, which is also the length of the chord.
Step-by-step explanation:
To find the length of the chord of the larger circle which touches the smaller circle, we can use the property that the angle between a tangent and a chord drawn from the point of contact is 90 degrees. Using this property, we can draw a line connecting the centers of the two circles, and it will be perpendicular to the chord. Let's call the point of intersection of this line and the chord as P.
Notice that the line connecting the centers of the circles and the chord form a right triangle. The radius of the larger circle is 5 cm and the radius of the smaller circle is 3 cm. We can use the Pythagorean theorem to find the length of the line connecting the centers of the circles.
Using the Pythagorean theorem:
(5 cm)^2 = (3 cm)^2 + (OP)^2
The length of the line connecting the centers of the circles (OP) is 4 cm. Since the line connecting the centers of the circles is perpendicular to the chord, the chord is the same length as the line connecting the centers of the circles.
Therefore, the length of the chord of the larger circle which touches the smaller circle is 4 cm.