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).
Statements: K * D, D $ N, N % M, M © W
Conclusions: I.M % W II.M $ W III.N @ D�...
Statements: O > M = Q > S; M ≥ K > A; Q ≤ O < E
Conclusions: I. O > S II. K < O �...
Statements: V ≥ W > X = Y, C > D = E ≥ V
Conclusions :I. E ≥ W II. D ≥ Y III. C > V
Statements: K = L ≥ Q; P < R ≤ S = Q; T = U ≤ P
Conclusions:
I. K > R
II. T < QStatements:
A = B ≤ Y < Z; P ≤ I < A; M ≤ Y < N
Conclusions:
I). M < Z
II). P < Y
III). N > A
...Statements: B & Y, Y # M, M $ X, X @ S
Conclusions: I. X $ Y II. X & Y
...Statements: I ≤ J = K < L < M, G ≥ H = I = T
Conclusions:
I. J > G
II. M = H
III. M > H
...Statements: A @ Z, Z # L, L % N, N @ U
Conclusions:
I. A @ N
II. Z @ U
III. A # L
Statement: B > C = J; B > S > E; B < N
Conclusion: I. E < C II. J ≤ E
In the question, assuming the given statements to be true, find which of the conclusion (s) among given two conclusions is/are definitely true and then...
