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In Fig. 4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. - Mathematics

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In Fig. 4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

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Solution

Diameter, AB = 13 cm

∴ Radius of the circle, `r=13/2=6.5 cm`

∠ACB is the angle in the semi-circle.

∴ ∠ACB = 90°

Now, in ACB, using Pythagoras theorem, we have

AB2=AC2= BC2

∴ (13)2=(12)2+(BC)2

∴ (BC)2 =(13)2-(12)2=169-144=25

∴ BC = `sqrt25=5cm`

Now, area of shaded region= Area of semi-circle- Are of ΔACB

`=1/2pir^2 -1/2xxBCxxAC`

`=1/2xx3.14xx(6.5)^2-1/2xx5xx12`

= 66.33-30

= 36.33 cm2

Thus, the area of the shaded region is 36.33 cm2 .

Concept: Circumference of a Circle
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