A chord, 7 cm long, is drawn in a circle with radius 3.7 cm . Calculate the distance of the chord from the centre of the circle. $$ \begin{array}{lll}0.7 \mathrm{~cm} & ext { B. } 1.2 \mathrm{~cm} & ext { C. } 20 \mathrm{~cm} \ ext { D. } 2.5 \mathrm{~cm}\end{array} $$

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A chord, 7 cm long, is drawn in a circle with radius 3.7 cm . Calculate the distance of the chord from the centre of the circle. $$ \begin{array}{lll}0.7 \mathrm{~cm} & 	ext { B. } 1.2 \mathrm{~cm} & 	ext { C. } 20 \mathrm{~cm} \ 	ext { D. } 2.5 \mathrm{~cm}\end{array} $$

UpStudy AI · Accepted Answer

Let the chord length be $$ L = 7 $$ cm, and the radius of the circle be $$ r = 3.7 $$ cm.

1. The chord is bisected by a perpendicular from the center. Thus, half the chord is  
   $$
   \frac{L}{2} = \frac{7}{2} = 3.5 \text{ cm}.
   $$

2. In the right triangle formed by the radius, the half-chord, and the perpendicular distance $$ d $$ from the center to the chord, the Pythagorean theorem gives:  
   $$
   d^2 + \left(\frac{L}{2}\right)^2 = r^2.
   $$

3. Substitute the known values:  
   $$
   d^2 + (3.5)^2 = (3.7)^2.
   $$

4. Calculate the squares:  
   $$
   (3.5)^2 = 12.25 \quad \text{and} \quad (3.7)^2 = 13.69.
   $$

5. Solve for $$ d^2 $$:  
   $$
   d^2 = 13.69 - 12.25 = 1.44.
   $$

6. Take the square root:  
   $$
   d = \sqrt{1.44} = 1.2 \text{ cm}.
   $$

Thus, the distance of the chord from the center of the circle is $$ \boxed{1.2 \text{ cm}} $$.
The distance of the chord from the center of the circle is 1.2 cm.

A chord, 7 cm long, is drawn in a circle with radius 3.7 cm . Calculate the distance
of the chord from the centre of the circle.

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