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
a. 3 cm
b. 6 cm
c. 9 cm
d. 1 cm
Solution:
Given, the radii of two concentric circles are 4 cm and 5 cm.
We have to find the length of each chord of one circle which is tangent to the other circle.
Consider two concentric circles.
OA = 4 cm
OB = 5 cm
From the figure,
OA ⟂ BC
In triangle OAB,
The triangle OAB is a right triangle with A at right angle.
OB² = OA² + AB²
(5)² = (4)² + AB²
25 = 16 + AB²
AB² = 25 - 16
AB² = 9
Taking square root,
AB = 3 cm
We know, BC = 2AB
So, BC = 2(3)
BC = 6 cm
Therefore, the length of each chord is 6 cm.
✦ Try This: Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.1 Problem 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 a. 3 cm, b. 6 cm, c. 9 cm, d. 1 cm
Summary:
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 6 cm
☛ Related Questions:
- In Fig. 9.3, if ∠AOB = 125°, then ∠COD is equal to a. 62.5°, b. 45°, c. 35°, d. 55°
- In Fig. 9.4, AB is a chord of the circle and AOC is its diameter such that ∠ACB = 50°. If AT is the . . . .
- From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pai . . . .