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If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal to
- a)60°
- b)70°
- c)80°
- d)90°
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If TP and TQ are two tangents to a circle with centre O so that ∠P...
If TP and TQ are two tangents to a circle with center O, it implies that both TP and TQ are perpendicular to the radius of the circle that passes through the point of tangency.
Let's say the points of tangency are A and B, with TP being tangent at A and TQ being tangent at B.
Since the tangents to a circle from an external point are equal in length, we have TA = TB.
Now, consider triangle TOA and triangle TOB.
TO is the radius of the circle, and OA and OB are radii drawn to the points of tangency.
Since radii of a circle are equal in length, we have OA = OB.
Also, both triangles share the side TO.
By SAS (side-angle-side) congruence, we can conclude that triangle TOA is congruent to triangle TOB.
Therefore, angle AOT is congruent to angle BOT.
Since TP is perpendicular to OA and TQ is perpendicular to OB, angles AOT and BOT are right angles.
Hence, TP and TQ are perpendicular to the radius of the circle that passes through the point of tangency.
Let's say the points of tangency are A and B, with TP being tangent at A and TQ being tangent at B.
Since the tangents to a circle from an external point are equal in length, we have TA = TB.
Now, consider triangle TOA and triangle TOB.
TO is the radius of the circle, and OA and OB are radii drawn to the points of tangency.
Since radii of a circle are equal in length, we have OA = OB.
Also, both triangles share the side TO.
By SAS (side-angle-side) congruence, we can conclude that triangle TOA is congruent to triangle TOB.
Therefore, angle AOT is congruent to angle BOT.
Since TP is perpendicular to OA and TQ is perpendicular to OB, angles AOT and BOT are right angles.
Hence, TP and TQ are perpendicular to the radius of the circle that passes through the point of tangency.
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If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer?.
If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then, ∠PTQ is equal toa)60°b)70°c)80°d)90°Correct answer is option 'B'. Can you explain this answer?.
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