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In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC?
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In the fig. above AB=AC , BD=DC and O is centre of circle . if angle A...
Given Information
- AB = AC (Isosceles triangle)
- BD = DC (Isosceles triangle)
- O is the center of the circle
- Angle ACO = 35°
Findings
To find angles ABD and BDC, we can use the properties of isosceles triangles and the angles in a circle.
Step 1: Analyzing Triangle ACO
- Since AB = AC, triangle ACO is isosceles.
- In triangle ACO, angle AOC = 2 * angle ACO (Angle at the center theorem).
- Therefore, angle AOC = 2 * 35° = 70°.
Step 2: Finding Angle ABC
- In triangle ABC, the exterior angle (angle AOB) is equal to the sum of the opposite interior angles (angle ACO + angle ABC).
- Hence, angle ABC = angle AOB - angle ACO.
- But angle AOB = angle AOC + angle ABC = 70° + angle ABC.
- Thus, we have angle ABC + 35° = 70°, leading to angle ABC = 35°.
Step 3: Finding Angle ABD
- Since BD = DC, triangle BDC is also isosceles.
- Therefore, angle BDC = angle ABD.
- The sum of angles in triangle ABC gives us:
angle ABC + angle ABD + angle ACB = 180°.
- Substituting angle ABC = 35° and angle ACB = 35°, we find:
35° + angle ABD + 35° = 180°.
- This simplifies to angle ABD = 180° - 70° = 110°.
Step 4: Finding Angle BDC
- Since triangle BDC is isosceles with BD = DC, angle BDC = angle ABD = 110°.
Final Angles
- Angle ABD = 110°
- Angle BDC = 110°
This concludes the calculation of angles in the given geometric configuration.
- AB = AC (Isosceles triangle)
- BD = DC (Isosceles triangle)
- O is the center of the circle
- Angle ACO = 35°
Findings
To find angles ABD and BDC, we can use the properties of isosceles triangles and the angles in a circle.
Step 1: Analyzing Triangle ACO
- Since AB = AC, triangle ACO is isosceles.
- In triangle ACO, angle AOC = 2 * angle ACO (Angle at the center theorem).
- Therefore, angle AOC = 2 * 35° = 70°.
Step 2: Finding Angle ABC
- In triangle ABC, the exterior angle (angle AOB) is equal to the sum of the opposite interior angles (angle ACO + angle ABC).
- Hence, angle ABC = angle AOB - angle ACO.
- But angle AOB = angle AOC + angle ABC = 70° + angle ABC.
- Thus, we have angle ABC + 35° = 70°, leading to angle ABC = 35°.
Step 3: Finding Angle ABD
- Since BD = DC, triangle BDC is also isosceles.
- Therefore, angle BDC = angle ABD.
- The sum of angles in triangle ABC gives us:
angle ABC + angle ABD + angle ACB = 180°.
- Substituting angle ABC = 35° and angle ACB = 35°, we find:
35° + angle ABD + 35° = 180°.
- This simplifies to angle ABD = 180° - 70° = 110°.
Step 4: Finding Angle BDC
- Since triangle BDC is isosceles with BD = DC, angle BDC = angle ABD = 110°.
Final Angles
- Angle ABD = 110°
- Angle BDC = 110°
This concludes the calculation of angles in the given geometric configuration.
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In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC?
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In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC? 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 fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC?.
In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC? 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 fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the fig. above AB=AC , BD=DC and O is centre of circle . if angle ACO=35° then find angle ABD and angle BDC?.
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