The perpendicular distance from the center of a circle to a chord is 5 cm. If the length of the chord is 24 cm, find the radius of the circle. Also, calculate the distance of another chord of length 18 cm from the center.

Correct option is B

Given:
Perpendicular distance to the first chord = 5 cm
Length of the first chord = 24 cm
Length of the second chord = 18 cm
Formula Used:
The perpendicular from the center of a circle to a chord bisects the chord.
Radius r = $$\sqrt{d^2 + (\frac{L}{2})^2}$$​​
where d is the perpendicular distance and L is the length of the chord.
Solution:
For the first chord, half of its length is $$\frac{24}{2}$$​ = 12 cm.
Using the Pythagorean theorem in the right-angled triangle formed by the radius, half-chord, and perpendicular distance:
r = $$\sqrt{5^2 + 12^2}$$​​
r = $$\sqrt{25 + 144}$$​​
r = $$\sqrt{169}$$​ = 13 cm.
Now, calculate the distance for the second chord of length 18 cm.
Half of its length is $$\frac{18}{2}$$​ = 9 cm.
Using the same theorem to find the new perpendicular distance $$d_2$$​:
​$$d_2 = \sqrt{r^2 - 9^2}$$​​
​$$d_2 = \sqrt{13^2 - 9^2}$$​​
​$$d_2 = \sqrt{169 - 81}$$​​
​$$d_2 = \sqrt{88}$$​​
$$d_2 = \sqrt{4 × 22} = 2\sqrt{22}$$​ cm
Final Answer
So the correct answer is (b)