Question

In the figure 7.47, seg AB is a chord of
a circle with centre P. If PA = 8 cm and
distance of chord AB from the centre P is 4 cm, find the area of the shaded portion.
( = 3.14, 3 = 1.73)​

Answer 1

Answer:

since we know that , distance from the centre of chord will bisect the chord and cut at 90° .

Let it cut at point O.

so,

now , by pythagoras theoram in ∆ AOP , we have

AO = √8²-4² = √48 = 4√3 cm

now,

in ∆ AOP again,

sin@ = PO/AB (@ = angle PAO)

sin@ = 1/2 = sin30

so, @ = 30°

it means , angle APO = 60°

so, angle at centre will be APB = 120°

now,

Area of minor sector = @/260(πr²) = 120/360(π8²)

= 1/3*3.14*64

= 66.98cm²

Now,

Area of isosceles ∆ APB = 1/2*Base*Height

= 1/2*8√3*4

= 10.38cm²

so,

shaded area = minor sector - area of ∆

= 66.98-10.38

= 56.6 cm² (Ans)

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