Q. 113.8( 16 Votes )

# Prove that two different circles cannot intersect each other at more than two points.

Answer :

Let two different circles intersect at three distinct points A, B and C.

Then, these points are already non-collinear.

A unique circle can be drawn to pass through these points. This is a contradiction.

Hence, two different circles cannot intersect each other at more than two points.

Rate this question :

In the given figure, is the center of the circle and

Calculate the values of (i) (ii)

RS Aggarwal & V Aggarwal - Mathematics

Prove that two different circles cannot intersect each other at more than two points.

RS Aggarwal & V Aggarwal - MathematicsProve that there is one and only one circle passing through three non – collinear points.

RS Aggarwal & V Aggarwal - MathematicsIn the adjoining figure, chords and of a circle with center intersect at right angles at If calculate

RS Aggarwal & V Aggarwal - Mathematics

Number of circles that can be drawn through three non-collinear points is

RD Sharma - MathematicsIn the given figure, is a diameter of a circle with center If and are straight lines, meeting at such that and find

(i) (ii) (iii)

RS Aggarwal & V Aggarwal - Mathematics

In the given figure, is an isosceles triangle in which and a circle passing through and intersects and at and respectively.

Prove that

RS Aggarwal & V Aggarwal - Mathematics

In the given figure, Show that is equal to the radius of the circumcircle of whose center is O.

RS Aggarwal & V Aggarwal - Mathematics

In the adjoining figure, is the center of a circle, and find

RS Aggarwal & V Aggarwal - Mathematics

In the given figure, and are straight lines through the center of a circle. If and find (i) (ii)

RS Aggarwal & V Aggarwal - Mathematics