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In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =?
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In the given figure, O is the centre of a circle IF - D * AC = 54 deg ...
Understanding the Circle and Angles
In the given figure, we need to find angle BAC using the provided angles: angle IF - D * AC = 54 degrees and angle ACB = 63 degrees.
Circle Properties
- O is the center of the circle, making AO and BO radii.
- The angle at the center (angle AOB) is twice the angle at the circumference (angle ACB).
Calculate Angle AOB
- Since angle ACB = 63 degrees, we can find angle AOB:
- Angle AOB = 2 * angle ACB
- Angle AOB = 2 * 63 degrees = 126 degrees.
Using the Exterior Angle Theorem
- In triangle ABC, angle BAC can be found using the exterior angle theorem:
- Angle AOB (exterior) = angle ACB + angle BAC.
- Therefore, 126 degrees = 63 degrees + angle BAC.
Solving for Angle BAC
- Rearranging the equation gives us:
- Angle BAC = 126 degrees - 63 degrees
- Angle BAC = 63 degrees.
Conclusion
- Thus, the measure of angle BAC is 63 degrees. This angle is derived from understanding the relationship between angles subtended at the center and the circumference of the circle, along with the application of the exterior angle theorem in triangle ABC.
In the given figure, we need to find angle BAC using the provided angles: angle IF - D * AC = 54 degrees and angle ACB = 63 degrees.
Circle Properties
- O is the center of the circle, making AO and BO radii.
- The angle at the center (angle AOB) is twice the angle at the circumference (angle ACB).
Calculate Angle AOB
- Since angle ACB = 63 degrees, we can find angle AOB:
- Angle AOB = 2 * angle ACB
- Angle AOB = 2 * 63 degrees = 126 degrees.
Using the Exterior Angle Theorem
- In triangle ABC, angle BAC can be found using the exterior angle theorem:
- Angle AOB (exterior) = angle ACB + angle BAC.
- Therefore, 126 degrees = 63 degrees + angle BAC.
Solving for Angle BAC
- Rearranging the equation gives us:
- Angle BAC = 126 degrees - 63 degrees
- Angle BAC = 63 degrees.
Conclusion
- Thus, the measure of angle BAC is 63 degrees. This angle is derived from understanding the relationship between angles subtended at the center and the circumference of the circle, along with the application of the exterior angle theorem in triangle ABC.
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In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =?
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In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =?.
In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the given figure, O is the centre of a circle IF - D * AC = 54 deg and angle ACB = 63 deg then angle BAC =?.
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