Answer to Question #200178 in Geometry for fiona

Question #200178

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


1
Expert's answer
2021-06-01T06:51:09-0400

Perimeter of triangle = 52.2 cm52.2\space cm

Let radius of circle = RR

R+R+AB=52.2R+R+AB=52.2

2R=52.2AB=282R=52.2-AB=28

R=14 cmR=14\space cm

AOB=2sin1(12.114)\angle AOB=2\sin^{-1}\bigg(\dfrac{12.1}{14}\bigg)

=2×59.801=119.6°=2\times59.801\\=119.6\degree


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