A chord with a length of $5$ runs from $pi/12$ to $pi/8$ radians on a circle. What is the area of the circle?

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Answer 1 · 2018-05-18T15:18:11

$color(blue)(pi((5sin((23pi)/48))/(sin(pi/24)))^2$

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From diagram:

$theta=pi/8-(pi)/12=pi/24$

We need to find radius $bbr$ :

We have an isosceles triangle with angle at the apex of $pi/24$

Two remaining angles are:

$(pi-(pi/24))/2=(23pi)/48$

Using sine rule:

$sin(pi/24)/5=sin((23pi)/48)/r$

$r=(5sin((23pi)/48))/(sin(pi/24))$

Area of circle is:

$pi((5sin((23pi)/48))/(sin(pi/24)))^2~~4590.212958$

A chord with a length of 5 5 runs from pi/12 pi/12 to pi/8 pi/8 radians on a circle. What is the area of the circle?