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Question
The radius of a circle is given as 15 cm and chord AB subtends an angle of 131° at the centre C of the circle. Using trigonometry, calculate:
- the length of AB;
- the distance of AB from the centre C.
Solution
Given, CA = CB = 15 cm, ∠ACB = 131°
Drop a perpendicular CP from center C to the chord AB.
Then CP bisects ∠ACB as well as chord AB.
∴ ∠ACP = 65.5°
In ΔACP,
`(AP)/(AC) = sin(65.5^circ)`
`=>` AP = 15 × 0.91 = 13.65 cm
i. AB = 2AP
= 2 × 13.65
= 27.30 cm.
ii. CP = AP cos (65.5°)
= 15 × 0.415
= 6.22 cm.
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