1. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
3 cm
6 cm
9 cm
1 cm
Step 1: The two circles are concentric. This means they have the same centre.
Step 2: The radius of the smaller circle is given as 4 cm, and the radius of the bigger circle is 5 cm.
Step 3: A chord of the bigger circle which just touches (is tangent to) the smaller circle will be at a distance of 4 cm (the radius of the smaller circle) from the centre.
Step 4: We know the formula for the length of a chord at a perpendicular distance d from the centre of a circle of radius R:
Chord length = \(2 \sqrt{R^2 - d^2}\)
Step 5: Here, the radius of the bigger circle is \(R = 5\) cm and the distance of the chord from the centre is \(d = 4\) cm.
Step 6: Substitute the values:
Chord length = \(2 \sqrt{5^2 - 4^2}\)
= \(2 \sqrt{25 - 16}\)
= \(2 \sqrt{9}\)
= \(2 \times 3\)
= 6 cm
Final Answer: The length of each such chord is 6 cm.