Question

A chord of length 16 cm is at a distance of 6 cm from the center of a circle. What is the length of the radius?

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 14 cm

Answer 1

Answer:

B. 10 cm

To find the length of the radius of the circle, we can use the geometric property relating the center, the chord,and the radius.

Given Data:

• Length of the chord = $16\text{ cm}$

• Distance of the chord from the center ($d$) = $6\text{ cm}$

Step-by-Step Calculation:

1. Apply the chord bisecting property: A perpendicular line drawn from the center of a circle to a chord bisects the chord.

   
   

   $\text{Half of the chord} (c) = \frac{16}{2} = 8\text{ cm}$

2. Set up a right-angled triangle: The radius ($r$), the distance from the center ($d$), and half of the chord ($c$) form a right-angled triangle, where the radius is the hypotenuse.

3. Use the Pythagorean theorem:

   
   

   $r^2 = d^2 + c^2$

   $r^2 = 6^2 + 8^2$

   $r^2 = 36 + 64$

   $r^2 = 100$

   $r = \sqrt{100} = 10\text{ cm}$

Answer:

The length of the radius is $10\text{ cm}$.