If PA and PB are tangents to the circle with the centre O such that angle APB = 50°, then angle OAB is equal to
Take your Class 10th Maths preparation to the next level with NCERT solutions and MCQ-based questions from Chapter 10: Circles. Solve exercise questions, short-answer problems and detailed explanations to master concepts like tangents, chords and their properties. These resources align with the CBSE syllabus, ensuring thorough exam preparation. Regular practice will sharpen your problem-solving skills and boost your confidence for board exams. Access step-by-step solutions and revision notes tailored to simplify learning and help students excel. Focus on understanding the properties of circles and their applications to strengthen your foundation. Begin practicing today to achieve excellent results and secure higher scores in exams. Start now!
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We are given:
– PA and PB are tangents to the circle with center O,
– Angle ∠APB = 50°.
Key property of tangents
The tangents PA and PB are equally inclined to the line joining the external point P to the center O. Therefore:
∠APO = ∠BPO = ∠APB / 2.
Substitute ∠APB = 50°:
∠APO = ∠BPO = 50° / 2 = 25°.
Relationship between angles
In triangle OAB:
– OA and OB are radii of the circle, so triangle OAB is isosceles.
– The angle ∠OAB is equal to ∠APO because the tangent PA is perpendicular to the radius OA.
Thus:
∠OAB = ∠APO = 25°.
This question is linked to Chapter 10 of the Class 10th NCERT Mathematics textbook, which is on the topic of “Circles.” Respond with an answer that reflects your understanding of the chapter.
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https://www.tiwariacademy.in/ncert-solutions/class-10/maths/