A chord of a circle of radius 14 cm subtends an angle of 60 at the ceF

1.	A chord of a circle of radius 14 cm subtends an angle of 60 at the ceFind the area of the corresponding minor segment of the circle.(Use π , 22 and V3-1-73)7
Answer» AB is the Chord. Radii drawn from points A & B are making 90 degrees at the center of the circle. Thus ∆AOB is a right angl triangle with height and base both equal to radius ‘r’. = 14 cm Area of the small segment.(Green Area) = Total are covered by sector AoB – Area of the triangle AOB. Area of the sector AOB = (ᶿ/360) ∏r^2 Since ᶿ = 90 Area of the sector AOB = (90/360) 221414/7 = 154 Square cm Area of the Triangle AOB = height base / 2 = 14 * 14 / 2 = 98 Square cm. Area of the small segment.(Green Area) = 154 – 98 = 56 Square cm. Area of the big segment = Area of the circle - Area of the small segment.(Green Area) = 221414/7 – 56 = 316 – 56 = 260 Square cm.

A chord of a circle of radius 14 cm subtends an angle of 60 at the ceFind the area of the corresponding minor segment of the circle.(Use π , 22 and V3-1-73)7

Answer»

AB is the Chord. Radii drawn from points A & B are making 90 degrees at the center of the circle.

Thus ∆AOB is a right angl triangle with height and base both equal to radius ‘r’. = 14 cm

Area of the small segment.(Green Area) = Total are covered by sector AoB – Area of the triangle AOB.

Area of the sector AOB = (ᶿ/360) ∏*r^2

Since ᶿ = 90

Area of the sector AOB = (90/360) 22*14*14/7 = 154 Square cm

Area of the Triangle AOB = height * base / 2 = 14 * 14 / 2 = 98 Square cm. Area of the small segment.(Green Area) = 154 – 98 = 56 Square cm.

Area of the big segment = Area of the circle - Area of the small segment.(Green Area)

= 22*14*14/7 – 56 = 316 – 56 = 260 Square cm.