Question

a chord of length 12cm subtends an angle of 78.2° at the centre of a circle. Find the radius of the circle.

Answer 1

this requires some circle geometry and then some trigonometry

to perpendicular from the centre to the chord bisect the chord.

the perpendicular will also bisect the subtended angle.



do you have a right triangle and you need to find the radius r

with the opposite side 6 and the angle being 39.1 degrees

hope this helps

Answer 2

the alternative method is to use the rule of sines

the triangle is isosceles because of equal radii... and so the base angles are

180 - 78.2 = 101.8
--------- -----
2 2


so using the law of sine

\[\frac{12}{\sin(78.2)} = \frac{r}{\sin(50.9)}\]

just solve for r