Question

In the diagram below, a circle O diameter, AB and radii OC are drawn. The length of AB is 12 in the measure of angle COD is 20°. if AC is congruent to BD find the area of a sector BOD in terms of pi.

Answer 1

Answer: = 8
`\pi`

Explanation:

The length of AB is 12, which is the diameter, so

r=6

You need to find the angle of BOD. It is on the bottom half. Also, AOC is the same angle

180-20 =160 now divide by 2

<BOD=80

In order to find area you multiply the fractional portion by the area

A(BOD) =
`(80)/(360) \pi r^(2)`

=
`(8)/(36) \pi 6^(2)` I reduced by 10 and the 36's cancel out

= 8
`\pi`