Question
Download Solution PDFAB is a chord of a circle with centre O. C is a point on the circumference of the circle in the minor sector. If ∠ABO = 40°, what is the measure (in degree) of ∠ACB?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠ABO = 40°
Concept:
The angle subtended by an arc at the center is double than subtended by it on other parts of the circle. In the figure below, ∠ AOB = 2∠ACB
Calculation:
In the figure ∠ABO = ∠BAO (angles formed by the radius are equal)
In Δ AOB, ∠ABO + ∠BAO + ∠BOA = 180°
⇒ ∠BOA = 180° - (40 + 40) = 100°
⇒ ∠BOA (external) = 360° - 100° = 260°.
∠ACB = \(1\over 2\) ∠BOA (external) (since angle formed by the arc at the center is double compared to the angle formed by the arc at other points on the circumference).
∴ ∠ACB = \(1\over 2\) × 260° = 130°
∴ The angle formed by ∠ACB is 130°.
Last updated on Jun 13, 2025
-> The SSC CGL Notification 2025 has been released on 9th June 2025 on the official website at ssc.gov.in.
-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.
-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.
-> The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.
-> Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the CGL exam form.
-> Candidates can refer to the CGL syllabus for a better understanding of the exam structure and pattern.
-> The CGL Eligibility is a bachelor’s degree in any discipline.
-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.
-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.
-> Candidates should also use the SSC CGL previous year papers for a good revision.