Skip to main content

Theorem 2

Theorem 1. There is one and only one circle passing through three non-collinear points.

Given:- A, B and C are three non-collinear points

To prove:- One and only one circle are drawn through the points A, B and C.

Construction:- AB and BC are joined PL and QM are drawn perpendicular bisectors respectively of AB and BC to intersect at O.
OA, OB and OC are joined.

Proof:- O lie on PL, the perpendicular bisector of AB

OA = OB ........................(i)

similarty OB = OC...........................(ii)

from (i) and (ii)

OA = OB = OC = r, say

A circle is drawn taking O as centre and r as radius to pass through A, B and C.

Let there be another centre O’ and another radius s, of circle through A, B and C. O’ must lie on PL and QM. As two lines can intersect at only one point. Hence O and O’ coincide.

OA = O' A = r = s

Hence there is unique circle passing through A, B and C.

 

www.cbsekey.com
Other Educational Portals
English | cbse | Science | Mathematics
Labels:

Comments

Post a Comment

Popular posts from this blog

Chivvy (Class VII - English Honeycomb - Chapter 4)

NCERT Textbook Exercise Questions (Important only) Working with the Poem Q.2: The last two lines of the poem are not prohibitions or instructions. What is the adult now asking the child to do? Do you think the poet is suggesting that this is unreasonable? Why? Ans: In the last two lines the adults are asking the child to think himself and to be independent in taking decisions in some matters. The adults are asking to be firm and determined which is unreasonable because they themselves don’t allow the child to take any decision. They always tell him what to do or what not to do. So, their asking the child to make up his own mind is totally unreasonable. Q.3: Why do you think grown-ups say the kind of things mentioned in the poem? Is it important that they teach children good manners, and how to behave in public? Ans: The grown-ups say such kind of things to their children in order to teach those good manners, etiquettes and how to behave in public. It is important to teach the children ...
30 comments
Read more