In a circle, the length of a chord is 12 cm and the perpendicular distance from the centre of the circle to the chord is 5 cm. What is the radius of the circle? (Rounded up to two decimal places.)​

Correct option is A

Given:

Length of chord = 12 cm

Perpendicular distance from centre to chord = 5 cm

Required: Radius (R) of the circle (to two decimal places)

Formula Used:

For a chord, with perpendicular distance (d) from the centre and half-chord =$$\frac{c}{2}:$$​​
​$$R^2 = d^2 + \left(\frac{c}{2}\right)^2$$​​

Solution:

Half of the chord =$$\frac{12}{2}$$​= 6 cm.

Apply Pythagoras in the right triangle formed by radius, distance, and half-chord:
​$$R^2 = 5^2 + 6^2 = 25 + 36 = 61$$​​
R $$= \sqrt{61} \approx 7.8102\ \text{cm}$$​​

Rounded to two decimal places: 7.81 cm.