We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Given an arc with a measure of 60◦ whose endpoints are at (1, 5) and (5, 3), find the area of the circle that contains the arc.

Confusedperson Nov 4, 2018

#1**+2 **

Distance between (1, 5) and 5, 3) =

sqrt [ ( 5 - 1)^2 + ( 5 - 3)^2 ] =

sqrt [ 4^2 + 2^2] = sqrt [ 20]

And if we connect these two points with a chord as well as drawing two radii to each point from the center of the circle, we will have an equilateral triangle....and since this triangle will have equal sides, the radii will have the same length as the chord

So....the area of the circle = pi * radius^2 = pi * ( sqrt(20) ) ^2 = 20 pi units^2 ≈ 62.83 units^2

CPhill Nov 4, 2018