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प्रश्न
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)
उत्तर
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 .
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