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Two circles are said to be congruent, if and only if:
- a)They have equal radius
- b)They are intersections,
- c)They are having equal length of common chord
- d)They are non-intersecting.
Correct answer is option 'A'. Can you explain this answer?
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Two circles are said to be congruent, if and only if:a)They have equal...
Understanding Congruent Circles
Congruent circles are defined as circles that have the same size and shape. The primary criterion for congruence in circles is their radius.
Key Points of Congruence:
- Equal Radius:
- Two circles are congruent if they have equal radii. This means that if you measure the distance from the center of each circle to its perimeter (the radius), and both measurements are the same, then the circles are congruent.
- Implications of Equal Radius:
- When two circles have equal radii, they will have the same area and circumference as well. This is a fundamental property of circles defined by their radius.
Why Other Options Are Not Valid:
- Intersections:
- Congruence does not depend on whether the circles intersect. They can intersect at zero, one, or two points but still be congruent if their radii are equal.
- Common Chord Length:
- The length of a common chord does not determine congruence. Two non-congruent circles can have the same chord length if they intersect in such a way.
- Non-Intersecting Circles:
- Two circles can be non-intersecting and still be congruent if they are positioned differently (e.g., one is offset from the other), but both have the same radius.
Conclusion:
The only definitive condition for two circles to be congruent is that they have equal radii. This criterion ensures that the circles are identical in size and shape, which is the essence of congruence in geometry.
Congruent circles are defined as circles that have the same size and shape. The primary criterion for congruence in circles is their radius.
Key Points of Congruence:
- Equal Radius:
- Two circles are congruent if they have equal radii. This means that if you measure the distance from the center of each circle to its perimeter (the radius), and both measurements are the same, then the circles are congruent.
- Implications of Equal Radius:
- When two circles have equal radii, they will have the same area and circumference as well. This is a fundamental property of circles defined by their radius.
Why Other Options Are Not Valid:
- Intersections:
- Congruence does not depend on whether the circles intersect. They can intersect at zero, one, or two points but still be congruent if their radii are equal.
- Common Chord Length:
- The length of a common chord does not determine congruence. Two non-congruent circles can have the same chord length if they intersect in such a way.
- Non-Intersecting Circles:
- Two circles can be non-intersecting and still be congruent if they are positioned differently (e.g., one is offset from the other), but both have the same radius.
Conclusion:
The only definitive condition for two circles to be congruent is that they have equal radii. This criterion ensures that the circles are identical in size and shape, which is the essence of congruence in geometry.
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Two circles are said to be congruent, if and only if:a)They have equal...
Two circles are congruent if they have equal radii.
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Two circles are said to be congruent, if and only if:a)They have equal radiusb)They are intersections,c)They are having equal length of common chordd)They are non-intersecting.Correct answer is option 'A'. Can you explain this answer?
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