A circle has a center at (1 ,2 ) and passes through (4 ,7 ). What is the length of an arc covering pi /4 radians on the circle?

1 Answer
Ratnaker Mehta
Jul 10, 2016

Length of Arc=sqrt34*pi/4~=4.58unit

Explanation:

Let us denote by S the Circle, by r radius, and pt.C(1,2)= Centre of S, and a pt P(4,7) on S

Then, dist. CP=r, and, using Dist. Formula, we get,

r^2=CP^2=(4-1)^2+(7-2)^2=9+25=34, giving r=sqrt34

The arc subtends angle theta = pi/4 at the centre, so that,

Length of Arc=r*theta=sqrt34*pi/4~=5.84*3.14/4=4.58unit

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