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A chord 12 cm long is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is (SSC CHSL 2013)
- a)16 cm
- b)8 cm
- c)6 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
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A chord 12 cm long is drawn in a circle of diameter 20 cm. The distanc...
Introduction
To find the distance of a chord from the center of a circle, we can use the properties of circles and right triangles.
Given Data
- Diameter of the circle: 20 cm
- Radius of the circle: 10 cm (since radius = diameter/2)
- Length of the chord: 12 cm
Steps to Calculate the Distance
1. Identify the Structure
- Draw a circle and mark its center O.
- Draw the chord AB, which is 12 cm long.
- Let point M be the midpoint of the chord AB.
2. Apply the Right Triangle Property
- The radius OM is the line from the center O to the midpoint M of the chord AB.
- Triangle OMA is a right triangle where:
- OA is the radius (10 cm)
- AM is half the chord length (12 cm / 2 = 6 cm)
- OM is the distance from the center to the chord.
3. Use the Pythagorean Theorem
- According to the Pythagorean theorem:
OA² = OM² + AM²
Substituting the values:
10² = OM² + 6²
100 = OM² + 36
OM² = 64
OM = √64 = 8 cm
Conclusion
The distance of the chord from the center of the circle is 8 cm. Thus, the correct answer is option 'B'.
To find the distance of a chord from the center of a circle, we can use the properties of circles and right triangles.
Given Data
- Diameter of the circle: 20 cm
- Radius of the circle: 10 cm (since radius = diameter/2)
- Length of the chord: 12 cm
Steps to Calculate the Distance
1. Identify the Structure
- Draw a circle and mark its center O.
- Draw the chord AB, which is 12 cm long.
- Let point M be the midpoint of the chord AB.
2. Apply the Right Triangle Property
- The radius OM is the line from the center O to the midpoint M of the chord AB.
- Triangle OMA is a right triangle where:
- OA is the radius (10 cm)
- AM is half the chord length (12 cm / 2 = 6 cm)
- OM is the distance from the center to the chord.
3. Use the Pythagorean Theorem
- According to the Pythagorean theorem:
OA² = OM² + AM²
Substituting the values:
10² = OM² + 6²
100 = OM² + 36
OM² = 64
OM = √64 = 8 cm
Conclusion
The distance of the chord from the center of the circle is 8 cm. Thus, the correct answer is option 'B'.
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Community Answer
A chord 12 cm long is drawn in a circle of diameter 20 cm. The distanc...
Given, AB = 12 cm; CD = 20 cm
OE = ?
Now, AE = EB = 6cm (The line drawn from centre of circle to the chord bisect the chord)
In ΔOAE, By Pythagoras theorem
(OA)2 = (OE)2 + (AE)2 ⇒ (10)2 = (OE)2 + (6)2
100 – 36 = (OE)2 ⇒ 64 = OE2 ⇒ OE = 8 cm
OE = ?
Now, AE = EB = 6cm (The line drawn from centre of circle to the chord bisect the chord)
In ΔOAE, By Pythagoras theorem
(OA)2 = (OE)2 + (AE)2 ⇒ (10)2 = (OE)2 + (6)2
100 – 36 = (OE)2 ⇒ 64 = OE2 ⇒ OE = 8 cm
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A chord 12 cm long is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is (SSC CHSL 2013)a)16 cmb)8 cmc)6 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?
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