Embibe Experts Solutions for Chapter: Circle, Exercise 2: Exercise

The equation of circumcircle of an equilateral triangle is $x^2+y^2+2gx+2fy+c=0$ and one vertex of the triangle is $(1,1),$ the equation of incircle of the triangle is

Let the base $AB$ of a triangle $ABC$ be fixed and the vertex $C$ lie on a fixed circle of radius $r$. Lines through $A$ and $B$ are drawn to intersect $CB$ and $CA,$ respectively, at $E$ and $F$ such that $CE:EB=1:2$ and $CF:FA=1:2$ If the point of intersection $P$ of these lines lies on the median through $AB$ for all positions of $AB$ then the locus of $P$ is

Six points $\left(x_i,y_i\right), i=1, 2\dots \dots \dots , 6$ are taken on the circle $x^2+y^2=4$ such that $\sum _{i=1}^6{x}_i=8$ and $\sum _{i=1}^6{y}_i=4$, the line segment joining orthocentre of a triangle made by any three points and the centroid of the triangle made by other three points passes through a fixed point $(h,k),$ then $h+k$ is

A circle with radius $\left|a\right|$ and centre on $y$-axis slides along it and a variable lines through $(a,0)$ cuts the circle at points $P$ and $Q.$ The region in which the point of intersection of tangents to the circle at points $P$ and $Q$ lies is represented by

The centres of a set of circle, each of radius $3,$ lies on the circle $x^2+y^2=25,$ The locus of any point in the set is

The coordinates of two points $P$ and $Q$ are $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ and $O$ is the origin. If circles be described on $OP$ and $OQ$ as diameters, then the length of their common chord is

If the circumference of the circle $x^2+y^2+8x+8y-b=0$ is bisected by the circle $x^2+y^2-2x+4y+a=0,$ then $a+b$ equals to

The equation of the circle passing through the point of intersection of the circle $x^2+y^2=4$ and the line $2x+y=1$ and having minimum possible radius is