Question

Two perpendicular chords both 5cm from the circle divides the circle into four parts. Compute the area of the sector containing the smallest part if the radius of the circle is 13cm

Answer 1

Area of sector CBE = Area of sector OCB - Area of triangle OCB + Area of triangle CEB

Answer 2

FB = sqrt(OB^2 - OF^2) = sqrt(13^2 - 5^2) = sqrt(144) = 12
FE = 5 (given)
EB = FB - FE = 12 - 5 = 7
Similarly, EC = 7

Answer 3

CB = sqrt(EB^2 + EC^2) = sqrt(7^2 + 7^2) = sqrt(2*7^2) = 7sqrt(2)
Angle COB can be found from the law of cosines:
CB^2 = OC^2 + OB^2 - 2(OC)(OB)cosCOB
49*2 = 13^2 + 13^2 - 2*13^2*cos(COB)
Find angle COB
Area of sector COB will be: Area of circle * angle COB / 360

Area of triangle COB = 1/2 * 13 * (13 * sin(angle COB))

Area of triangle CEB = 1/2 * EB * EC = 1/2 * 7 * 7

Put them all in the formula for the the area of sector CBE

Answer 4

Thank you! I finally got it..

Answer 5

you are welcome.