Question
Download Solution PDFIn the figure given below, O is the centre of the circle. If ∠APQ = 35°, find the value of ∠OQP.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFAccording to the alternate segment theorem, the angle between a tangent and a chord at the point of contact is equal to the angle made by the chord in the alternate segment of the circle
In the figure given,
⇒ ∠APQ = ∠QRP = 35°
As we know, the angle subtended by an arc at the centre of the circle is twice the angle subtended by the arc at any other point on the circle
⇒ ∠QOP = 2 × ∠QRP = 2 × 35° = 70°
Now, considering ΔOQP,
∵ OQ = OP = radius of circle
⇒ ΔOQP is an isosceles triangle
⇒ ∠OQP = ∠OPQ
∵ Sum of angles of triangle = 180°
⇒ ∠QOP + ∠OQP + ∠OPQ = 180°
∴ ∠OQP = (180° – 70°)/2 = 110°/2 = 55°
Last updated on Jun 11, 2025
-> RRB NTPC 2025 Exam Postponed. Railway Recruitment Board has rescheduled the RRB NTPC Exam for June 5, 2025 (Shift 3).
-> RRB NTPC Exam Analysis 2025 is LIVE now. All the candidates appearing for the RRB NTPC Exam 2025 can check the complete exam analysis to strategize their preparation accordingly.
-> The UPSC Prelims Result 2025 and UPSC IFS Result 2025 has been released @upsc.gov.in
-> The RRB NTPC Admit Card 2025 has been released on its official website.
-> Candidates who will appear for the RRB NTPC Exam can check their RRB NTPC Time Table 2025 from here.
-> The RRB NTPC CBT 1 Exam is scheduled from 5th June to 24th June 2025 as per the revised tentative exam schedule.
-> The RRB NTPC 2025 Notification has been released for a total of 11558 vacancies.
-> A total of 3445 Vacancies have been announced for Undergraduate posts like Commercial Cum Ticket Clerk, Accounts Clerk Cum Typist, Junior Clerk cum Typist & Trains Clerk.
-> A total of 8114 vacancies are announced for Graduate-level posts in the Non-Technical Popular Categories (NTPC) such as Junior Clerk cum Typist, Accounts Clerk cum Typist, Station Master, etc.
-> Prepare for the exam using RRB NTPC Previous Year Papers.
-> Check out the Rajasthan PTET Admit Card 2025 and UPSC Prelims Result Date 2025 here.