Asked by Marky
A circle is divided into two parts by a chord, 3cm a wat from the center. Find the area of the smaller part if the circle has an area of 201cm squared.
Answers
Answered by
Reiny
Did you make your sketch?
Complete the central triangle with the chord as its base
let the central angle be 2Ø
area of whole circle = πr^2 = 201
r = √(201/π)
cosØ = 3/√(201/π) = ....
Ø = appr ....
2Ø = .....
we can find the area of the central triangle:
= (1/2)(r)(r)sin(2Ø) = ......
Also the area of the sector using ratios:
2Ø/360° = sector/210
sector = 210Ø/180
subtract the triangle area from the sector area and you have the segment area
I will leave all that calculation stuff up to you
Complete the central triangle with the chord as its base
let the central angle be 2Ø
area of whole circle = πr^2 = 201
r = √(201/π)
cosØ = 3/√(201/π) = ....
Ø = appr ....
2Ø = .....
we can find the area of the central triangle:
= (1/2)(r)(r)sin(2Ø) = ......
Also the area of the sector using ratios:
2Ø/360° = sector/210
sector = 210Ø/180
subtract the triangle area from the sector area and you have the segment area
I will leave all that calculation stuff up to you