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suppose you are given a circle .given a construction to find its centre.
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suppose you are given a circle .given a construction to find its centr...
The below given steps will be followed to find the centre of the given circle.
Step1. Take the given circle.
Step2. Take any two different chords AB and CD of this circle and draw perpendicular bisectors of these chords.
Step3. Let these perpendicular bisectors meet at point O. Hence, O is the centre of the given circle.
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suppose you are given a circle .given a construction to find its centr...
Finding the Center of a Circle
To find the center of a given circle, you can use a simple geometric construction involving chords. Here’s how to do it step-by-step:
Materials Needed
- Compass
- Ruler
- Pencil
Steps to Construct
- Draw a Chord:
- Using a ruler, draw a straight line segment that connects two points on the circumference of the circle. This line is called a chord.
- Find the Midpoint:
- Measure the length of the chord and find its midpoint. You can do this by measuring the distance from each endpoint to the midpoint or by folding the chord in half.
- Construct a Perpendicular Bisector:
- Place the compass point on one end of the chord and draw an arc above and below the chord. Without changing the compass width, repeat this from the other end of the chord. The arcs should intersect above and below the chord.
- Draw the Perpendicular Line:
- Using a ruler, draw a straight line through the points of intersection of the arcs. This line is the perpendicular bisector of the chord.
- Repeat with Another Chord:
- To ensure accuracy, repeat the above steps with a different chord. The point where the two perpendicular bisectors intersect is the center of the circle.
Conclusion
This method effectively uses basic geometric principles to locate the center of any circle. By constructing perpendicular bisectors of two different chords, you can confidently determine the circle's center.
To find the center of a given circle, you can use a simple geometric construction involving chords. Here’s how to do it step-by-step:
Materials Needed
- Compass
- Ruler
- Pencil
Steps to Construct
- Draw a Chord:
- Using a ruler, draw a straight line segment that connects two points on the circumference of the circle. This line is called a chord.
- Find the Midpoint:
- Measure the length of the chord and find its midpoint. You can do this by measuring the distance from each endpoint to the midpoint or by folding the chord in half.
- Construct a Perpendicular Bisector:
- Place the compass point on one end of the chord and draw an arc above and below the chord. Without changing the compass width, repeat this from the other end of the chord. The arcs should intersect above and below the chord.
- Draw the Perpendicular Line:
- Using a ruler, draw a straight line through the points of intersection of the arcs. This line is the perpendicular bisector of the chord.
- Repeat with Another Chord:
- To ensure accuracy, repeat the above steps with a different chord. The point where the two perpendicular bisectors intersect is the center of the circle.
Conclusion
This method effectively uses basic geometric principles to locate the center of any circle. By constructing perpendicular bisectors of two different chords, you can confidently determine the circle's center.
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