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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such ∠POR = 120∘, then ∠OPQ is
- a)45∘
- b)30∘
- c)60∘
- d)35∘
Correct answer is option 'B'. Can you explain this answer?
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PQ is a tangent drawn from a point P to a circle with centre O and QOR...
That angle QPR is 30 degrees.
To prove this, we can use the properties of tangents and angles in a circle.
Since PQ is a tangent to the circle, it is perpendicular to the radius drawn from the center of the circle to the point of tangency. Therefore, angle QOR is a right angle.
Since QOR is a diameter of the circle, angle QOR is also a central angle and its measure is twice the measure of angle QPR. So, angle QPR is half of angle QOR.
Since angle QOR is a right angle, its measure is 90 degrees. Therefore, angle QPR is half of 90 degrees, which is 45 degrees.
Since we are given that angle QPR is 30 degrees, this is a contradiction. Therefore, it is not possible for angle QPR to be 30 degrees.
To prove this, we can use the properties of tangents and angles in a circle.
Since PQ is a tangent to the circle, it is perpendicular to the radius drawn from the center of the circle to the point of tangency. Therefore, angle QOR is a right angle.
Since QOR is a diameter of the circle, angle QOR is also a central angle and its measure is twice the measure of angle QPR. So, angle QPR is half of angle QOR.
Since angle QOR is a right angle, its measure is 90 degrees. Therefore, angle QPR is half of 90 degrees, which is 45 degrees.
Since we are given that angle QPR is 30 degrees, this is a contradiction. Therefore, it is not possible for angle QPR to be 30 degrees.
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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer?
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PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer? 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 PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer?.
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer? 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 PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such∠POR = 120∘, then∠OPQ isa)45∘b)30∘c)60∘d)35∘Correct answer is option 'B'. Can you explain this answer?.
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