Prove that two circles cannot intersect at mo | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(N/A) Assume that two circles intersect at three distinct points,$A$,$B$,and $C$. Since $A$,$B$,and $C$ are three distinct points,they are non-colline

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) Assume that two circles intersect at three distinct points,$A$,$B$,and $C$.
Since $A$,$B$,and $C$ are three distinct points,they are non-collinear.
According to the geometric theorem,there is one and only one circle that passes through three non-collinear points.
Therefore,if two circles pass through the same three points $A$,$B$,and $C$,they must be the same circle.
This contradicts the assumption that there are two distinct circles.
Hence,it is impossible for two distinct circles to intersect at more than two points.

Prove that two circles cannot intersect at more than two points.

Similar Questions

In the figure,$BC$ is a diameter of the circle and $\angle BAO = 60^{\circ}$. Then $\angle ADC$ is equal to: (in $^{\circ}$)

In a cyclic quadrilateral $ABCD$,$\angle A = 4 \angle C$ and $\angle B = 3 \angle D$. Find all the angles of $ABCD$.

If two chords $AB$ and $CD$ of a circle intersect at right angles (see Fig.),prove that $\text{arc } CXA + \text{arc } DZB = \text{arc } AYD + \text{arc } BWC = \text{semicircle}$.

Write True or False and justify your answer in each of the following: Two chords $AB$ and $CD$ of a circle are each at distances $4 \ cm$ from the centre. Then $AB = CD$.

$O$ is the circumcentre of the triangle $ABC$ and $D$ is the mid-point of the base $BC$. Prove that $\angle BOD = \angle A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module