Question

Find the area of the segment of a circle of radius 12cm whose corresponding sector has a central angle

of 60​

Answer 1

Answer:

AsectorOABhasitsradiusr=OA=OB=12cmandthecentralangleAOB=600.Tofindout−ar.segmentAPB=?Solution−InΔABCwehaveOA=OB(radiiofthesamecircle).∴∠OAB=∠OBA⟹∠OAB+∠OBA=2∠OAB.Now∠AOB+∠OAB+∠OBA=600+2∠OAB=180O(anglesumpropertyoftriangles).⟹2∠OAB=120O⟹∠OAB=∠OBA=600.∴ΔAOBisanequilateralonewithsidea=12cm.Soar.ΔAOB=43a2=43122cm