A chord of length 60 cm is at a distance of 16 cm from the centre of a circle. What is the radius (in cm) of the circle?a)17b)34c)51d)68Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given Information:
A chord of length 60 cm is at a distance of 16 cm from the centre of a circle.

Formula:
The formula to find the radius of a circle when the length of the chord and the distance from the centre of the circle to the chord are given is:
$$ r = \sqrt{h(2r - h)} $$
where r is the radius of the circle and h is the distance from the centre of the circle to the chord.

Calculation:
- Given: Length of chord, c = 60 cm
- Given: Distance from the centre to the chord, h = 16 cm
- Using the formula, we have:
$$ r = \sqrt{16(2r - 16)} $$
$$ r = \sqrt{32r - 256} $$
$$ r^2 = 32r - 256 $$
$$ r^2 - 32r + 256 = 0 $$

- Solving this quadratic equation using the quadratic formula:
$$ r = \frac{-(-32) \pm \sqrt{(-32)^2 - 4*1*256}}{2*1} $$
$$ r = \frac{32 \pm \sqrt{1024 - 1024}}{2} $$
$$ r = \frac{32}{2} $$
$$ r = 16 $$

Therefore, the radius of the circle is 16 cm.

Conclusion:
The correct option is:
b) 34

Top Courses for SSC

Suggested Free Tests

Related Content

Mock Test Series

Related Question Answers

Other Engg Branches

Related Exams

Company