In a circle, a ten cm long chord is at a distance of 12 cm from the centre of the circle. Length of the diameter of the circle (in
cm) is:
This questions was previously asked in
SSC CGL 17th August 2021 Shift-3
Explanation:
- To find the length of the diameter, consider a right triangle formed by the radius, half of the chord, and the perpendicular distance from the center to the chord.
- The chord is 10 cm, so half of it is 5 cm.
- The perpendicular from the center is 12 cm.
- Use the Pythagorean theorem: \(r^2 = 5^2 + 12^2\).
- Solving gives \(r^2 = 25 + 144 = 169\).
- Thus, \(r = \sqrt{169} = 13\) cm.
- The diameter is twice the radius, so \(2 \times 13 = 26\) cm.
- 26 cm (Option 3) is the correct length of the diameter.
![]()
By: santosh