Question

The radius of a circle is given as 15 cm and chord ab subtends an angle of 131degree at the centre c using trignometry calculate length of ab and the distance of ab from centre c

Answer 1

Solution:-
Consider the circle with radius equal to 15 cm with center 'O' and AB be the chord which subtends an angle of 131° at the center of the circle.
As we know that perpendicular from the center of the chord bisects the chord.
Let AB = x cm
⇒ AC = x/2 cm
∠ AOB = 131°
∴ ∠ AOC = 131°/2 = 65.5°
In Δ AOC,
sin (65.5°) = x/15*2
⇒ x = 0.909 × 30    (As sin 65.5° = .909)
⇒ x = 27.27 cm
So, the length of AB is 27.27 cm
cos (65.5°) = OC/15
⇒ OC = .414 × 15
OC = 6.21 cm 
Hence, the length of chord AB is 27.27 cm and distance between the center and the chord is 6.21 cm.
Answer

Answer 2

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