Answer to Question #200178 in Geometry for fiona

Question

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

Answer 1

Perimeter of triangle = $52.2\space cm$

Let radius of circle = $R$

$R+R+AB=52.2$

$2R=52.2-AB=28$

$R=14\space cm$

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

$=2\times59.801\\=119.6\degree$