Question
In a circle of radius 13 cm, a chord has length 10 cm.
Find: (a) the distance of the chord from the centre, (b) the angle subtended by the chord at the centre (in degrees, correct to nearest degree).Solution
(a) Let distance from centre O to chord AB be d, and M be midpoint of AB. OM ⟂ AB, AM = 10/2 = 5 cm Right triangle OMA: OA² = OM² + AM² 13² = d² + 5² 169 = d² + 25 ⇒ d² = 144 ⇒ d = 12 cm (b) Let central angle ∠AOB = θ. Chord length: AB = 2R sin(θ/2) 10 = 2×13×sin(θ/2) 10 = 26 sin(θ/2) sin(θ/2) = 10/26 = 5/13 θ/2 = sin⁻¹(5/13) ≈ 22.62° ⇒ θ ≈ 45.24° So angle ≈ 45° (nearest degree).
Who has won the BBC Sports Personality of the Year 2021 Award?
The UH-3H helicopter of the Indian Navy was de-inducted after how many years of service?
What rank did India achieve in the Network Readiness Index (NRI) 2024?
Which state will host Hornbill Festival in December 2021?
Who is appointed as the chairman of the Insurance Regulatory and Development Authority of India (IRDAI)?
What is the name of Russia’s newly tested nuclear-powered cruise missile?
SEBI has approved the launch of the beta version of T+0 settlement on an optional basis. What does T+0 settlement signify?
What is the total number of job vacancies mobilised by the National Career Service (NCS) portal since its launch?
According to the World Happiness Report 2023, which country is the happiest country in the world?
Which bank has recently announced to launch of BoB World Gold, a new feature on its mobile banking platform designed especially for seniors and the elde...
