Mathematics - Circle Question with Solution | TestHub

Use $A=(0,4),B=(-3,0),C=(3,0),P=(x,y)$. Inside the triangle, the distances to $AB$ and $AC$ are $(12+4x-3y)/5$ and $(12-4x-3y)/5$. Thus $25y^2=(12-3y{)}^2-16x^2$, or $2x^2+2y^2+9y-18=0$. Only the short arc from $B$ to $C$ with $y>0$ lies inside the triangle.