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Length of chord MN is 40 cm. Distance of chord MN from the centre is 15 cm. What will be the radius of this circle?
- a)42 cm
- b)32 cm
- c)30 cm
- d)25 cm
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Length of chord MN is 40 cm. Distance of chord MN from the centre is 1...
Given:
The distance of chord MN from the center is 15 cm
The length of chord MN is 40 cm
Concept:
Chord length using perpendicular distance from the centre = 2 × √ (r2 – d2) [∵ r = radius, d = perpendicular distance]
Calculation:
Length of Chord = 2 × √ (r2 – d2)
40 = 2 × √ (r2 – 152) = 25 cm
∴ Option 4 is the correct answer.
The distance of chord MN from the center is 15 cm
The length of chord MN is 40 cm
Concept:
Chord length using perpendicular distance from the centre = 2 × √ (r2 – d2) [∵ r = radius, d = perpendicular distance]
Calculation:
Length of Chord = 2 × √ (r2 – d2)
40 = 2 × √ (r2 – 152) = 25 cm
∴ Option 4 is the correct answer.
Most Upvoted Answer
Length of chord MN is 40 cm. Distance of chord MN from the centre is 1...
Given:
The distance of chord MN from the center is 15 cm
The length of chord MN is 40 cm
Concept:
Chord length using perpendicular distance from the centre = 2 × √ (r2 – d2) [∵ r = radius, d = perpendicular distance]
Calculation:
Length of Chord = 2 × √ (r2 – d2)
40 = 2 × √ (r2 – 152) = 25 cm
∴ Option 4 is the correct answer.
The distance of chord MN from the center is 15 cm
The length of chord MN is 40 cm
Concept:
Chord length using perpendicular distance from the centre = 2 × √ (r2 – d2) [∵ r = radius, d = perpendicular distance]
Calculation:
Length of Chord = 2 × √ (r2 – d2)
40 = 2 × √ (r2 – 152) = 25 cm
∴ Option 4 is the correct answer.
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Community Answer
Length of chord MN is 40 cm. Distance of chord MN from the centre is 1...
Given data:
- Length of chord MN = 40 cm
- Distance of chord MN from the centre = 15 cm
Formula:
- The radius of a circle can be calculated using the formula: \( r = \frac{1}{2} \times \sqrt{2h(2R - h)} \), where r is the radius, h is the distance of the chord from the center, and R is the length of the chord.
Calculations:
Given that the length of the chord MN is 40 cm and the distance of the chord from the center is 15 cm.
- Substituting the values in the formula, we get:
\( r = \frac{1}{2} \times \sqrt{2 \times 15(2 \times 40 - 15)} \)
\( r = \frac{1}{2} \times \sqrt{30 \times 65} \)
\( r = \frac{1}{2} \times \sqrt{1950} \)
\( r = \frac{1}{2} \times 44.18 \)
\( r = 22.09 \) cm
Therefore, the radius of the circle is approximately 22.09 cm, which is closest to option 'D' - 25 cm.
- Length of chord MN = 40 cm
- Distance of chord MN from the centre = 15 cm
Formula:
- The radius of a circle can be calculated using the formula: \( r = \frac{1}{2} \times \sqrt{2h(2R - h)} \), where r is the radius, h is the distance of the chord from the center, and R is the length of the chord.
Calculations:
Given that the length of the chord MN is 40 cm and the distance of the chord from the center is 15 cm.
- Substituting the values in the formula, we get:
\( r = \frac{1}{2} \times \sqrt{2 \times 15(2 \times 40 - 15)} \)
\( r = \frac{1}{2} \times \sqrt{30 \times 65} \)
\( r = \frac{1}{2} \times \sqrt{1950} \)
\( r = \frac{1}{2} \times 44.18 \)
\( r = 22.09 \) cm
Therefore, the radius of the circle is approximately 22.09 cm, which is closest to option 'D' - 25 cm.
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Length of chord MN is 40 cm. Distance of chord MN from the centre is 15 cm. What will be the radius of this circle?a)42 cmb)32 cmc)30 cmd)25 cmCorrect answer is option 'D'. Can you explain this answer?
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