9) In the given figure, O is the centre and AOC is a diameter of the circle Find - Maths - Areas Related to Circles

Question

9) In the given figure, O is the centre and AOC is a diameter of
the circle Find

(i) the sum of the areas of the two shaded segments made by the
chords AB and BC
(ii) the area of the shaded segment made by the chord PQ t a k e ,
π = 22 7

Shruti Tyagi · Accepted Answer

Dear student,

In △ABC,AC2=AB2+BC2AC2=42+42AC2=16+16=32AC=42cmthus, OA=OC=42cm2=22cmOB =OA=OC each radius of circlethus OB=22cm∴ area of triangle =12×42×22=8cmNow, area of semi circle=πr22 =227×2×22×22=887cm2=12
5cm2thus, area of shaded portion =area of semicircle -area of triangle=12
5-8=4
5cm2hence, the sum of the area of two shaded segments made by chord AB and BC=4
5cm2

Regards

9) In the given figure, O is the centre and AOC is a diameter of the circle . Find (i) the sum of the areas of the two shaded segments made by the chords AB and BC. (ii) the area of the shaded segment made by the chord PQ. t a k e , π = 22 7

9) In the given figure, O is the centre and AOC is a diameter of the circle . Find

(i) the sum of the areas of the two shaded segments made by the chords AB and BC.
(ii) the area of the shaded segment made by the chord PQ. $[t a k e, π = \frac{22}{7}]$