A chord with a length of $13$ runs from $pi/12$ to $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2018-06-13T02:47:47

$color(brown)("Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"$

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$"Given ; " hat (AOB) = pi/2 - pi/12 = (5pi)/12, vec(AB) = 13$

$hat (AOM) = hat (AOB) / 2 = (5pi)/24$

$bar(OA) = r = bar(AM) / sin (AOM) = (bar(AB)/2) / sin (AOM)$

$r = (13/2) / sin ((5pi)/24) = 10.68 " units"$

$"Area of the circle " A_c = pi r^2 = pi * (10.68)^2 = 358.34 " sq units"$

A chord with a length of 13 13 runs from pi/12 pi/12 to pi/2 pi/2 radians on a circle. What is the area of the circle?