# Circles

## Radical Axis of Two circles – Definition and Formula

Here you will learn what is the formula to find the equation of radical axis of two circles. Let’s begin – Radical Axis of Two Circles Definition : The locus of a point, which moves in such a way that the length of tangents drawn from it to the circle are equal and is called …

## Pole and Polar of a Circle Equation

Here you will learn what is the pole and polar of a circle and pole of given line with respect to a circle. Let’s begin – Pole and Polar of a Circle Let any straight line through the given point A$$(x_1, y_1)$$ intersects the given circle S = 0 in two points P and Q …

## Chord of Contact of Circle – Length and Equation

Here you will learn equation of chord of contact of circle and length of chord of contact of circle. Let’s begin – Equation of Chord of Contact A line joining the two points of contacts of two tangents drawn from a point outside the circle, is called chord of contact of that point. If two …

## Intercepts Cut by the Circle on Axes

Here you will learn intercept cut by the circle an the axes i.e. x-axis and y-axis respectively. Let’s begin – Intercept Cut by Circle on Axes The intercepts cut by the circle $$x^2 + y^2 + 2gx + 2fy + c$$ = 0 on : (i) x-axis x-axis = 2$$\sqrt{g^2 – c}$$ (ii) y-axis y-axis …

## Equation of Pair of Tangents to a Circle

Here you will learn what is the equation of pair of tangents to a circle from an external point with example. Let’s begin – Equation of Pair of Tangents to a Circle Let the equation of circle S = $$x^2$$ + $$y^2$$ – $$a^2$$ and P($$x_1,y_1$$) is any point outside the circle. From the point …

## Length of Tangent to a Circle Formula From an External Point

Here you will learn what is the length of tangent to a circle formula from an external point with example. Let’s begin – Length of Tangent to a Circle Formula The length of tangent drawn from point ($$x_1,y_1$$) outside the circle S = $$x^2 + y^2 + 2gx + 2fy + c$$ = 0 is, …

## Orthogonal Circles and Condition of Orthogonal Circles

Here you will learn what are orthogonal circles and condition of orthogonal circles. Let’s begin – Orthogonal Circles Let two circles are $$S_1$$ = $${x}^2 + {y}^2 + 2{g_1}x + 2{f_1}y + {c_1}$$ = 0 and $$S_2$$ = $${x}^2 + {y}^2 + 2{g_2}x + 2{f_2}y + {c_2}$$ = 0.Then Angle of intersection of two circles …

## Angle of Intersection of Two circles Formula

Here you will learn what is the formula for the angle of intersection of two circles. Let’s begin – Angle of Intersection of Two Circles Formula The angle between the tangents of two circles at the point of intersection of the two circles is called angle of intersection of two circles. If two circles are …