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:

1. the length of AB;
2. the distance of AB from the centre C.

Answer 1

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.