Question

6. The length of the minor arc AB of a circle, centre O, is 2π cm and the length of the major arc is 22π cm. Find:

a) the radius of the circle
b) the acute angle AOB. ​

Answer 1

a) 24 [cm]; b) 30°.

Explanation:

a) the length of full the circle is: min_arc(AB)+maj_arc(AB)=π(22+2)=24π [cm]. Then the radius is: r=L/π; ⇒ r=24π/π=24 [cm];

b) if the full circle is 360° (L=24π), then m(∠AOB):2=360°:24 and the required measure of the acute angle AOB is:

m(∠AOB)=360*(1/12)=30°.