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Question 23 - CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 13, 2024 by Teachoo

In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB = 75°.

 

 

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Question 23 In the given figure, O is the centre of circle. Find ∠AQB, given that PA and PB are tangents to the circle and ∠APB = 75°. We know that Radius is perpendicular to the tangent ∴ ∠ OAP = ∠ OBP = 90° In quadrilateral PAOB Sum of angles = 360° ∠ APB + ∠ OAP + ∠ OBP + ∠ AOB = 360° 75° + 90° + 90° + ∠ AOB = 360° 255° + ∠ AOB = 360° ∠ AOB = 360° − 255° ∠ AOB = 105° Also, We know that Angle subtended by an arc at the centre is double the angle subtended by the same arc at any point on the circle. ∴ ∠ AOB = 2 × ∠ AQB 105° = 2 × ∠ AQB 2 × ∠ AQB = 105° ∠ AQB = (105° )/2 ∠ AQB = 52.5°
  1. Class 10
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    3. CBSE Class 10 Sample Paper for 2023 Boards - Maths Standard

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo