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if tow circle intersect at tow points, prove that their centers lie on the perpendicular bi sector of the common chord
? Related: What is a Circle?
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if tow circle intersect at tow points, prove that their centers lie on...
Proof that the centers lie on the perpendicular bisector of the common chord:
Given: Two circles intersect at two points
To Prove: The centers of the circles lie on the perpendicular bisector of the common chord
Proof:
- Let the two circles intersect at points A and B, creating a common chord AB
- Let O1 and O2 be the centers of the circles
- Connect O1A, O1B, O2A, and O2B
- As O1A = O1B and O2A = O2B, OA and OB are the radii of the circles
- This creates two congruent triangles O1AO2 and O1BO2 by SSS congruence
- Therefore, angle O1AO2 = angle O1BO2
- This means that the line joining the centers O1 and O2 is perpendicular to the common chord AB
- Hence, the centers of the circles lie on the perpendicular bisector of the common chord
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if tow circle intersect at tow points, prove that their centers lie on the perpendicular bi sector of the common chord Related: What is a Circle??
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if tow circle intersect at tow points, prove that their centers lie on the perpendicular bi sector of the common chord Related: What is a Circle?? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about if tow circle intersect at tow points, prove that their centers lie on the perpendicular bi sector of the common chord Related: What is a Circle?? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for if tow circle intersect at tow points, prove that their centers lie on the perpendicular bi sector of the common chord Related: What is a Circle??.
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