SOLUTION: A 120� arc of a circle has end points (√6,0) and (0, -√6). How long is radius of this circle (in simplest form).

Question 1004217: A 120� arc of a circle has end points (√6,0) and (0, -√6). How long is radius of this circle (in simplest form).
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

Points and both are at distance from , the origin.
So, triangle is a right isosceles triangle, with angles at and .
Points and are on the same arc of a circle of radius ,
so both are at distance from the center of the circle, .
Since the center is at the same distance from and ,
the center is on the perpendicular bisector of ,
which contains , the midpoint of .
The perpendicular bisector of the base of an isosceles triangle passes through the vertex,
so the perpendicular bisector of AB is .
The distance from to is
,
so .
Adding point to the sketch and drawing isosceles triangle we get

, and as is an isosceles triangle,
altitude splits it into two congruent triangles: and .

, and .
Substituting the measures we know
, and since ,
--> .
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SOLUTION: A 120� arc of a circle has end points (&#8730;6,0) and (0, -&#8730;6). How long is radius of this circle (in simplest form).

SOLUTION: A 120� arc of a circle has end points (√6,0) and (0, -√6). How long is radius of this circle (in simplest form).