On circle below the measure of SV is 120°
What is the measure of VU
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Let (x−h)2+(y−k)2=r2 …………..(1)
where (h, k) is the centre of the circle and r is the radius.
Let us draw a line A(2,0) and B(4,0). If the centre lies outside the line AB then it is a chord.
The diameter of the circle is bigger than the chord. Suppose AB is the diameter of the circle then the centre of the circle must be a midpoint of AB.
∴ Using section formula
h=22+0=22=1
k=24+0=24=2
∴ Coordinates of the centre=(h,k)
=(1,2)
Equation (1) becomes,
(x−1)2+(y−2)2=r2 …………….(2)
Since (2) passes through (2,0), equation (2) can be written as,
(2−1)2+(0−2)2=r2
12+22=r2
1+4=r2
r2=5
r=5
Equation of the circle with minimum radius is
∴(x−1)2+(y−2
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