Question

in the given figure, O is the centre and AOC is a diameter of the circle. Find the sum of the areas
of two shaded segments made by the chords AB and BC..​

Answer 1

sum of the areas of two shaded segments = 4.57 cm²

Step-by-step explanation:

O is the centre and AOC is a diameter of the circle.

=> AB & BC chord will have a right angle at B  ( 180°/2 = 90°)

=> ΔABC is a right angle Triangle

Area of Δ ABC = (1/2) * AB * BC

= (1/2) * 4 * 4

= 8 cm²

AC² = AB² + BC²

=>AC² = 4² + 4²

=> AC² = 32

=> (AC/2)² = 8

=> radius² = 8

Area of Semicircle = (1/2)πr²  = (1/2)(22/7) * 8  = 88/7

sum of the areas of two shaded segments made by the chords AB and BC

= 88/7  - 7

= 32/7

= 4.57 cm²

learn more :

O is the centre of two concentric circles

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