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If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)
- a)55°
- b)60°
- c)65°
- d)50°
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If O be the circumcentre of a triangle PQR and ∠QOR = 110°, &a...
In ΔOPR, OP = OR = radius
∠OPR = ∠ORP = 25°
In ΔOQR OQ = OR = radius
∠OQR= ∠ORQ
∴ ∠PRQ = ∠PRO + ∠ORQ = 25° + 35° = 60°
Most Upvoted Answer
If O be the circumcentre of a triangle PQR and ∠QOR = 110°, &a...
Given Information:
- ∠QOR = 110°
- ∠OPR = 25°
To Find:
- ∠PRQ
Solution:
- The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of its sides.
- Since O is the circumcenter, the angles subtended by the same chord at the circumference are equal.
- Therefore, ∠QPR = 2∠QOR = 2 * 110° = 220° (Angle subtended by the same chord at the circumference)
- Also, ∠QPR = 180° - ∠OPR - ∠PRQ
- 220° = 180° - 25° - ∠PRQ
- ∠PRQ = 180° - 220° + 25°
- ∠PRQ = 5°
Therefore, the measure of ∠PRQ is 60° (Option B).
- ∠QOR = 110°
- ∠OPR = 25°
To Find:
- ∠PRQ
Solution:
- The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of its sides.
- Since O is the circumcenter, the angles subtended by the same chord at the circumference are equal.
- Therefore, ∠QPR = 2∠QOR = 2 * 110° = 220° (Angle subtended by the same chord at the circumference)
- Also, ∠QPR = 180° - ∠OPR - ∠PRQ
- 220° = 180° - 25° - ∠PRQ
- ∠PRQ = 180° - 220° + 25°
- ∠PRQ = 5°
Therefore, the measure of ∠PRQ is 60° (Option B).
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Community Answer
If O be the circumcentre of a triangle PQR and ∠QOR = 110°, &a...
In ΔOPR, OP = OR = radius
∠OPR = ∠ORP = 25°
In ΔOQR OQ = OR = radius
∠OQR= ∠ORQ
∴ ∠PRQ = ∠PRO + ∠ORQ = 25° + 35° = 60°
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If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer?.
If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer?.
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If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If O be the circumcentre of a triangle PQR and ∠QOR = 110°, ∠OPR = 25°, then the measure of ∠PRQ is (SSC CGL 1st Sit. 2013)a)55°b)60°c)65°d)50°Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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