Answer :

We know that,

Tangent drawn from an external point of a circle are equal

∴ OP = OQ = 10 cm

PQ = 5 + 5

= 10 cm

As OP = OQ = PQ

∴ OP = OQ = OP = 10 cm

Hence, POQ is an equilateral triangle as all the sides are equal to each other

Also, angles of an equilateral triangle are of 60^{o}

∴∠ POQ = 60^{o}

Here, we have

Side = 10 cm

Radius, r = 5 cm

⇒ θ = 60°

And, R = 10 cm

∴ Area of shaded region = Area of triangle OPQ + Area of semi-circle PBQM – Area of sector OPAQ

.

Hence, proved

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