AB is a chord of a circle O.If |AB|=24.2cm and the perimeter of triangle AOB is 52.2 cm,calculate angle AOB correct to the nearest degree
Perimeter of triangle = 52.2 cm52.2\space cm52.2 cm
Let radius of circle = RRR
R+R+AB=52.2R+R+AB=52.2R+R+AB=52.2
2R=52.2−AB=282R=52.2-AB=282R=52.2−AB=28
R=14 cmR=14\space cmR=14 cm
∠AOB=2sin−1(12.114)\angle AOB=2\sin^{-1}\bigg(\dfrac{12.1}{14}\bigg)∠AOB=2sin−1(1412.1)
=2×59.801=119.6°=2\times59.801\\=119.6\degree=2×59.801=119.6°
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