On the joining `(1,0)`a n d`(3,0)` be and equilateral triangle is drawn, having its vertex in the first quadrant. Find the equation to the circles described on its sides as diameter.

Explanation

In equilateral triangle, `a=b=c`

Equation of circle with sides as diameter is given by
`
(x−1)(x−2)+(y−0)(y−0)=0`
`\implies
x^2+y^2−3x+2=0`

Centre of circle,

`(h−1)^2+k^2=(h−2)^2+k^2=1`
`h= \frac{3}{2},k=\frac{\sqrt3}{2}`

On side BC,

`(x−2)(x−\frac{3}{2})+(y−0)(y−\frac{\sqrt3}{2})=0`
`\implies 2x^2+2y^2−7x−3y+6=0`

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