Another problem in C2-Radian measure & its application

In the diagram AB is the diameter of a circle, centre O and radius 2 cm. The point C is on the circumference such that angle COB = 2/3 π radians.

Click to see diagram. C2-Ch6-6B.8b.png

The shaded region enclosed by the chord AC, arc CB & AB is the template for a brooch.
Find the exact value of the perimeter of the brooch.

Reply 1

BingBangBong

geton

In the diagram AB is the diameter of a circle, centre O and radius 2 cm. The point C is on the circumference such that angle COB = 2/3 π radians.

Click to see diagram. C2-Ch6-6B.8b.png

The shaded region enclosed by the chord AC, arc CB & AB is the template for a brooch.
Find the exact value of the perimeter of the brooch.

So you want ACO.

Reply 2

BingBangBong

ACO is .5 x rsquared theta.

So that is .5 x 4 x one third pi
so that gives you two third pi for the area.

Reply 3

BingBangBong

O sorry I didnt read the question perimeter. You can work out CA by using the cosine rule. Angle COA is one third pi and CO and AO are 2 so you can work out CA by using the cosine rule. You then add this value to 4 to get the perimeter of that triangle.

Reply 4

Fatdaffodil

Original post by geton

In the diagram AB is the diameter of a circle, centre O and radius 2 cm. The point C is on the circumference such that angle COB = 2/3 π radians.

Click to see diagram. C2-Ch6-6B.8b.png