The radius of the circle can be calculated by using the formula:
Radius = Diameter/2 = 26cm/2 = 13cm
Let the distance from O to the center of the chord be h. This forms a right triangle with the radius of the circle.
Using Pythagoras theorem, we have:
(13)^2 = h^2 + (26/2)^2
169 = h^2 + 169
h^2 = 0
h = 0
This means that the chord PQ is a diameter of the circle, and it divides the circle into two equal halves.
The area of the minor segment formed by the chord PQ can be calculated by first finding the area of the sector formed by the chord PQ and then subtracting the area of the triangle formed by the sector.
The area of the sector:
Sector area = (θ/360) * π * r^2
Where θ is the angle subtended by the chord PQ at the center O.
In this case, θ = 180 degrees.
Sector area = (180/360) * (22/7) * (13)^2
Sector area = (1/2) * (22/7) * 169
Sector area = 1181
Area of the triangle:
Triangle area = (1/2) * base * height
Triangle area = (1/2) * 26 * 13
Triangle area = 169
Area of the minor segment = Sector area - Triangle area
Area of the minor segment = 1181 - 169
Area of the minor segment = 1012 cm^2
Therefore, the area of the minor segment formed by the chord PQ is 1012 cm^2 (correct to the nearest whole number).
The diameter of a circle centre is O is 26cm. If a chord PQ is drawn such that from O to the centre of the chord,calculate,correct to the nearest whole number Area of the minor segment formed by the chord PQ
Take π=22/7
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