CIRCLES PASSING THROUGH ONE, TWO, THREE POINTS.

By Md.Bilal

Circle : as per definition of circle it is a collection of points from a fixed point with equal distance.

circle does not having any sides or edges it is a two dimensional figure.

All of we have gone through the concepts regarding circle like radius, diameter, chord, interior and exterior of circle but today one more new concept we will study and that is tangent.

Before that in your textbook there are some activities which you have to complete.

let me help you to complete those.

ACTIVITY1 : 

In the adjoining figure, seg DE is
a chord of a circle with centre C.
seg CF ⊥ seg DE. If diameter of the
circle is 20 cm, DE =16 cm
find CF.

In 9th class we have studied properties of chords those are ,

• The perpendicular drawn from the center of a circle on its chord bisects the chord.  
• A segment joining the center of a circle and the mid point of circle is perpendicular to the chord.
• The chords of a circle which are equidistant from the center of the circle are congruent  

Now using above first two properties we have to solve the given activity.

Solution

In figure C is center of circle and DC and CE are radii of circle 

Given : diameter = DE = 20 

∴ radius =  
∴ DC = CE = 10
  seg CF ⊥ seg DE
we know that a perpendicular drawn from center of circle on its chord bisects chord.
∴  DF = FE = 8
now in Δ CDF 
ㄥCFD = 90        ( seg CF ⊥ seg DE) 
∴  By Pythagoras  theorem 

∴ CF = 6
Now you can easily solve Activity II.

CIRCLES PASSING THROUGH ONE, TWO, THREE POINTS :

Number of Circles passing through one point:

 this one is most simple question even you have tried this most of the time while playing with compass. the beautiful design can be formed if yet you have not tried then please try at once from a single point we can draw N no of circles that is we can  draw infinite circles.

Number of circles passing from two points:

see using two points A, B  draw a line segment AB and draw its perpendicular bisector l on that perpendicular bisector take any point keep your needle of compass on point and nip of your pencil on any point A, B draw a circle check if it passes through  other point or not taking  N number of points on line l you can draw N number of (infinite) circles passing through given two points.

Number of circles passing through 3 non- collinear points :

students you might have  study  about concept of non collinear points. the figure we can draw from three non collinear points is ?     Triangle
same way we have to  draw triangle after that we have to draw centro id of  triangle from that centroid you have to draw circle.
we have gone through construction of circumcircle  that we have to construct here but we can draw only one circle for one triangle that is from three non collinear points we can draw 1 circle.

Number of circles passing through 3 collinear points:

from three collinear points we can't draw a single circle. no circle can be drawn from three collinear points.