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In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF?
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In the circle with centre o . AB , CD,and EF are tangents to the circl...
Understanding the Circle and Tangents
In this scenario, we have a circle with center O and tangents AB, CD, and EF touching the circle at points G, H, and I respectively. The line GH is a diameter of the circle.
Properties of Tangents
- Tangents to a circle from a common external point are equal in length.
- The angle between a tangent and a radius drawn to the point of tangency is 90 degrees.
Establishing the Angles
- Since GH is a diameter, the angle subtended by it at any point on the circle is 90 degrees (Thales' theorem).
- Therefore, angles EGH and FGH are both right angles (90 degrees).
Finding Angle EOF
- Since GH is a straight line (diameter), angle EOF can be analyzed using the tangents.
- The angles formed between the tangents and the diameter give us two angles: EGH and FGH, both being 90 degrees.
- The angle EOF is actually the angle subtended by the tangents at the center O.
Conclusion
- Since EGH and FGH are both 90 degrees, they add up to 180 degrees at point O.
- Thus, angle EOF is the angle formed between the two tangents EF and GH, which equals 180 degrees.
In summary, the measure of angle EOF is 180 degrees, showing the relationship between the tangents and the diameter of the circle.
In this scenario, we have a circle with center O and tangents AB, CD, and EF touching the circle at points G, H, and I respectively. The line GH is a diameter of the circle.
Properties of Tangents
- Tangents to a circle from a common external point are equal in length.
- The angle between a tangent and a radius drawn to the point of tangency is 90 degrees.
Establishing the Angles
- Since GH is a diameter, the angle subtended by it at any point on the circle is 90 degrees (Thales' theorem).
- Therefore, angles EGH and FGH are both right angles (90 degrees).
Finding Angle EOF
- Since GH is a straight line (diameter), angle EOF can be analyzed using the tangents.
- The angles formed between the tangents and the diameter give us two angles: EGH and FGH, both being 90 degrees.
- The angle EOF is actually the angle subtended by the tangents at the center O.
Conclusion
- Since EGH and FGH are both 90 degrees, they add up to 180 degrees at point O.
- Thus, angle EOF is the angle formed between the two tangents EF and GH, which equals 180 degrees.
In summary, the measure of angle EOF is 180 degrees, showing the relationship between the tangents and the diameter of the circle.
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In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF?
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In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF?.
In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the circle with centre o . AB , CD,and EF are tangents to the circle at point G , H and I respectively . where GH is a diameter . find the measure of EOF?.
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