Given: sector bac with r=8

radius of inscribed circle o is 2

find the area of the sector bac

will put picture into description

Area of sector = 21.75 units.

Step-by-step explanation:

Given, BAC is a sector of radius 8.

⇒ AB = 8;  AC = 8.

Now, let a line from A passing through O meets the curve BC at P.

⇒AP = 8. (radius of sector).

Given, radius of inscribed circle is 2.

⇒AO = AP- OP = 8-2 = 6.

let the inscribed circle meets AB at Q. so, triangle AQO forms right angle triangle(since, AB is a tangent).

⇒ cos(∠AOQ) = 2/6 (adjacent / hypotenuse)

 ⇒ ∠AOQ = 70.53° ⇒ ∠OAQ = 180 - 90- 70.53 = 19.47°

⇒ total ∠A = 2× 19.47° = 38.94°.

⇒ area of sector = π×r²×, where r = 8

⇒ area of sector = 21.75 units.

4038

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