Can someone please help me. I'm behind and need to get caught up ☹️ 20 pts
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Answer:
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.