SOLUTION: The points X(3,4) and Y(9,1) lie on the circumference of a circle. There is exactly 60 degree of arc between X and Y. Find the radius of the circle.

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Question 985461: The points X(3,4) and Y(9,1) lie on the circumference of a circle. There is exactly 60 degree of arc between X and Y. Find the radius of the circle.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The center point of the circle is equally distant from both X and Y, forming an isosceles triangle; but since you have central angle being 60 degrees, this forces the other angles each to also be 60 degrees. This is then an equilateral triangle with points, X, Y, and the center of the circle. The radius will be the DISTANCE between X and Y, found using the distance formula. Now you know radius r.

r=sameAs=sqrt%28%289-3%29%5E2%2B%281-4%29%5E2%29
r=sqrt%2836%2B9%29
r=sqrt%2845%29
r=3sqrt%285%29

Next, simply form %286%2F36%29%282pi%2Ar%29 and compute or evaluate the length of arc.
(Fraction of the circumference)

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The points X(3,4) and Y(9,1) lie on the circumference of a circle. There is exactly 60 degree of arc between X and Y. Find the radius of the circle.
Line segment XY = 3%2Asqrt%285%29

With center O, radii OX and OY are congruent

With arc XY being 60%5Eo, central angle XOY also equals 60%5Eo

With radii OX and OY congruent, an equilateral triangle is formed

With line segment XY being 3%2Asqrt%285%29, radii also measure: highlight_green%283%2Asqrt%285%29%29